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Etale Cohomology Of Rigid Analytic Varieties And Adic Spaces

by Roland Huber

145,09€ + 10% CARD

 The aim of this book is to give an introduction to adic spaces and to develop systematically their Ã©tale cohomology. After this the basic results on the Ã©tale cohomology of adic spaces are proved: base change theorems, finiteness, PoincarÃ© duality, comparison theorems with the algebraic case.
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Frobenius Manifolds - Quantum Cohomology And Singularities

131,84€ + 10% CARD

 Frobenius Mannigfaltigkeiten - ein aktuelles Gebiet, das Algebraische Geometrie und Quanten Kohomologie verbindet, motiviert wurde es durch die Physik. Dieses Buch ist augenblicklich das einzige, das alle wichtigen Experten zusammenbringt und die verschieden thematischen Schwerpunkte zusammenstellt, es gibt einen hervorragenden Uberblick uber "the state of the art" dieses Forschungsgebietes.
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Lie Group Actions In Complex Analysis

by Dimitrij Akhiezer

52,99€ + 10% CARD

 This book was planned as an introduction to a vast area, where many contri butions have been made in recent years. The choice of material is based on my understanding of the role of Lie groups in complex analysis. On the one hand, they appear as the automorphism groups of certain complex spaces, e. g. , bounded domains in en or compact spaces, and are therefore important as being one of their invariants. On the other hand, complex Lie groups and, more generally, homoge neous complex manifolds, serve as a proving ground, where it is often possible to accomplish a task and get an explicit answer. One good example of this kind is the theory of homogeneous vector bundles over flag manifolds. Another example is the way the global analytic properties of homogeneous manifolds are translated into algebraic language. It is my pleasant duty to thank A. L. Onishchik, who first introduced me to the theory of Lie groups more than 25 years ago. I am greatly indebted to him and to E. B. Vinberg forthe help and advice they have given me for years. I would like to express my gratitude to M. Brion, B. GilIigan, P. Heinzner, A. Hu kleberry, and E. Oeljeklaus for valuable discussions of various subjects treated here. A part of this book was written during my stay at the Ruhr-Universitat Bochum in 1993. I thank the Deutsche Forschungsgemeinschaft for its research support and the colleagues in Bochum for their hospitality.
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Singular Nonlinear Partial Differential Equations

by Hidetoshi Tahara e Raymond Gerard

118,59€ + 10% CARD

 The aim of this book is to put together all the results that are known about the existence of formal, holomorphic and singular solutions of singular non linear partial differential equations. We study the existence of formal power series solutions, holomorphic solutions, and singular solutions of singular non linear partial differential equations. In the first chapter, we introduce operators with regular singularities in the one variable case and we give a new simple proof of the classical Maillet''s theorem for algebraic differential equations. In chapter 2, we extend this theory to operators in several variables. The chapter 3 is devoted to the study of formal and convergent power series solutions of a class of singular partial differential equations having a linear part, using the method of iteration and also Newton''s method. As an appli cation of the former results, we look in chapter 4 at the local theory of differential equations of the form xy'' = 1(x,y) and, in particular, we show how easy it is to find the classical results on such an equation when 1(0,0) = 0 and give also the study of such an equation when 1(0,0) #- 0 which was never given before and can be extended to equations of the form Ty = F(x, y) where T is an arbitrary vector field.
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Seminar On New Results In Nonlinear Partial Differential Equations - A Publication Of The Max-Planck-Institut Für Mathematik, Bonn

by Anthony Tromba

118,59€ + 10% CARD

 This book consists almost entirely of papers delivered at the Seminar on partial differential equations held at Max-Planck-Institut in the spring of 1984. They give an insight into important recent research activities. Some further developments are also included.
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From Gauss To Painleve - A Modern Theory Of Special Functions

by Hironobu Kimura, Katsunori Iwasaki, Masaaki Yoshida e Shun Shimemura

158,34€ + 10% CARD

 It contains modern treatments of the Gauss hypergeometric differential equation, monodromy of second order Fuchsian equations and nonlinear differential equations near singular points.The book starts from an elementary level requiring only basic notions of differential equations, function theory and group theory.
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Hypergeometric Functions, My Love - Modular Interpretations Of Configuration Spaces

by Masaaki Yoshida

86,11€ + 10% CARD

 Die klassische Geschichte der hypergeometrischen Funktionen, dem Raum der Konfigurationen von 4 Punkten auf der projektiven Geraden, elliptischen Kurven, Modulfunktionen und Theta Funktionen, wird in diesem Buch zur Geschichte der hypergeometrischen Funktionen in 4 Variablen, dem Raum der Konfigurationen von 6 Punkten in der projektiven Ebene, K3 Flachen, Theta Funktionen in 4 Variablen weiterentwickelt. Der Autor erzahlt die Geschichte in einem lebendigen Stil, beginnend von einem elementaren Niveau, so da Studenten angesprochen werden.
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Ball And Surface Arithmetics

by Rolf-Peter Holzapfel

59,61€ + 10% CARD

 This monograph is based on the work of the author on surface theory con nected with ball uniformizations and arithmetic ball lattices during several years appearing in a lot of special articles. The first four chapters present the heart of this work in a self-contained manner (up to well-known ba sic facts) increased by the new functorial concept of orbital heights living on orbital surfaces. It is extended in chapter 6 to an explicit HURWITZ theory for CHERN numbers of complex algebraic surfaces with the mildest singularities, which are necessary for general application and proofs. The chapter 5 is dedicated to the application of results in earlier chapters to rough and fine classifications of PICARD modular surfaces. For this part we need additionally the arithmetic work of FEUSTEL whose final results are presented without proofs but with complete references. We had help ful connections with Russian mathematicians around VENKOV, VINBERG, MANIN, SHAFAREVICH and the nice guide line of investigations of HILBERT modular surfaces started by HIRZEBRUCH in Bonn. More recently, we can refer to the independent (until now) study of Zeta functions of PICARD modular surfaces in the book [L-R] edited by LANGLANDS and RAMAKR ISHN AN. The basic idea of introducing arrangements on surfaces comes from the monograph [BHH], (BARTHEL, HOFER, HIRZEBRUCH) where linear ar rangements on the complex projective plane ]p2 play the main role.
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Moduli Of Curves And Abelian Varieties - The Dutch Intercity Seminar On Moduli

59,61€ + 10% CARD

 The present volume, with contributions of R. Dijkgraaf, C. Faber, G. van der Geer, R. Rain, E. Looijenga, and F. Oort, originates from the Dutch Intercity Seminar on Moduli (year 1995-96). Some of the articles here were discussed, in preliminary form, in the seminar; others are completely new. Two introductory papers, on moduli of abelian varieties and on moduli of curves, accompany the articles. Topics include a stratification of a moduli space of abelian varieties in positive characteristic, and the calculation of the classes of the strata, tautological classes for moduli of abelian varieties as well as for moduli of curves, correspondences between moduli spaces of curves, locally symmetric families of curves and jaco bians, and the role of symmetric product spaces in quantum field theory, string theory and matrix theory. This Intercity Seminar is part of the long term project "Algebraic curves and Riemann surfaces: geometry, arithmetic and applications" , sponsored hy the Netherlands Organization for Scientific Research (NWO), that has been running since 1994. Its ancestry can be traced back to joint activities in the seventies (if not earlier), which as of 1980 had evolved into active biweekly research seminars. These have been a focal point of Dutch algebraic geometry and singularity theory since. We are grateful to NWO for its support for the project. C.F. thanks the Max-Planck-Institut fur Mathematik, Bonn, for support during the final stages of the preparation of this volume.
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Automorphic Forms And The Picard Number Of An Elliptic Surface

by Peter F. Stiller

59,61€ + 10% CARD

 In studying an algebraic surface E, which we assume is non-singular and projective over the field of complex numbers t, it is natural to study the curves on this surface. In order to do this one introduces various equivalence relations on the group of divisors (cycles of codimension one). One such relation is algebraic equivalence and we denote by NS(E) the group of divisors modulo algebraic equivalence which is called the N~ron-Severi group of the surface E. This is known to be a finitely generated abelian group which can be regarded naturally as a subgroup of 2 H (E,Z). The rank of NS(E) will be denoted p and is known as the Picard number of E. 2 Every divisor determines a cohomology class in H(E,E) which is of I type (1,1), that is to say a class in H(E,9!) which can be viewed as a 2 subspace of H(E,E) via the Hodge decomposition. The Hodge Conjecture asserts in general that every rational cohomology class of type (p,p) is algebraic. In our case this is the Lefschetz Theorem on (I,l)-classes: Every cohomology class 2 2 is the class associated to some divisor. Here we are writing H (E,Z) for 2 its image under the natural mapping into H (E,t). Thus NS(E) modulo 2 torsion is Hl(E,n!) n H(E,Z) and th 1 b i f h -~ p measures e a ge ra c part 0 t e cohomology.
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Cauchy-Riemann Complex - Integral Formulae And Neumann Problem

by Ingo Lieb e Joachim Michel

59,61€ + 10% CARD

 Integral Formulae and Neumann Problem.
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Riemann-Hilbert Problem - A Publication From The Steklov Institute Of Mathematics Adviser: Armen Sergeev

by A. A. Bolibruch e D. V. Anosov

98,71€ + 10% CARD

 This book is devoted to Hilbert''s 21st problem (the Riemann-Hilbert problem) which belongs to the theory of linear systems of ordinary differential equations in the complex domain. The problem concems the existence of a Fuchsian system with prescribed singularities and monodromy. Hilbert was convinced that such a system always exists. However, this tumed out to be a rare case of a wrong forecast made by hirn. In 1989 the second author (A.B.) discovered a counterexample, thus 1 obtaining a negative solution to Hilbert''s 21st problem. After we recognized that some "data" (singularities and monodromy) can be obtai ned from a Fuchsian system and some others cannot, we are enforced to change our point of view. To make the terminology more precise, we shaII caII the foIIowing problem the Riemann-Hilbert problem for such and such data: does there exist a Fuchsian system having these singularities and monodromy? The contemporary version of the 21 st Hilbert problem is to find conditions implying a positive or negative solution to the Riemann-Hilbert problem.
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Algebraic Geometry And Its Applications - Proceedings Of The 8th Algebraic Geometry Conference, Yaroslavl’ 1992. A Publication From The Steklov Institute Of Mathematics. Adviser: Armen Sergeev

59,61€ + 10% CARD

 This volume consists of articles presented as talks at the Algebraic Geometry Conference held in the State Pedagogical Institute of Yaroslavl''from August 10 to 14, 1992. These conferences in Yaroslavl'' have become traditional in the former USSR, now in Russia, since January 1979, and are held at least every two years. The present conference, the eighth one, was the first in which several foreign mathematicians participated. From the Russian side, 36 specialists in algebraic geometry and related fields (invariant theory, topology of manifolds, theory of categories, mathematical physics etc. ) were present. As well modern directions in algebraic geometry, such as the theory of exceptional bundles and helices on algebraic varieties, moduli of vector bundles on algebraic surfaces with applications to Donaldson''s theory, geometry of Hilbert schemes of points, twistor spaces and applications to string theory, as more traditional areas, such as birational geometry of manifolds, adjunction theory, Hodge theory, problems of rationality in the invariant theory, topology of complex algebraic varieties and others were represented in the lectures of the conference. In the following we will give a brief sketch of the contents of the volume. In the paper of W. L. Baily three problems of algebro-geometric nature are posed. They are connected with hermitian symmetric tube domains. In particular, the 27-dimensional tube domain ''Fe is treated, on which a certain real form of E7 acts, which contains a "nice" arithmetic subgroup r e, as observed earlier by W. Baily.
ENGLISH

History Of Complex Dynamics - From Schröder To Fatou And Julia

by Daniel S. Alexander

79,49€ + 10% CARD

 In late 1917 Pierre Fatou and Gaston Julia each announced several results regarding the iteration ofrational functions of a single complex variable in the Comptes rendus of the French Academy of Sciences. These brief notes were the tip of an iceberg. In 1918 Julia published a long and fascinating treatise on the subject, which was followed in 1919 by an equally remarkable study, the first instalIment of a three part memoir by Fatou. Together these works form the bedrock of the contemporary study of complex dynamics. This book had its genesis in a question put to me by Paul Blanchard. Why did Fatou and Julia decide to study iteration? As it turns out there is a very simple answer. In 1915 the French Academy of Sciences announced that it would award its 1918 Grand Prix des Sciences mathematiques for the study of iteration. However, like many simple answers, this one doesn''t get at the whole truth, and, in fact, leaves us with another equally interesting question. Why did the Academy offer such a prize? This study attempts to answer that last question, and the answer I found was not the obvious one that came to mind, namely, that the Academy''s interest in iteration was prompted by Henri Poincare''s use of iteration in his studies of celestial mechanics.
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Conjectures In Arithmetic Algebraic Geometry - A Survey

by Wilfred W. J. Hulsbergen

79,49€ + 10% CARD

 In this expository text we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued math ematicians for a long period of time. Starting from Fermat''s Last Theorem one is naturally led to introduce L functions, the main, motivation being the calculation of class numbers. In partic ular, Kummer showed that the class numbers of cyclotomic fields play a decisive role in the corroboration of Fermat''s Last Theorem for a large class of exponents. Before Kummer, Dirichlet had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemann''s paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by properties of L-functions. Twentieth century number theory, class field theory and algebraic geome try only strengthen the nineteenth century number theorists''s view. We just mention the work of E. H~cke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlet''s L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generalization of Dirichlet''s L-functions with a generalization of class field theory to non-abelian Galois extensions of number fields in mind.
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Lectures On Nonlinear Evolution Equations - Initial Value Problem

by Reinhard Racke

59,61€ + 10% CARD

 The book in hand is based on lectures which were given at the University of Bonn in the winter semesters of 1989/90 and 1990/91. The aim of the lectures was to present an elementary, self-contained introduction into some important aspects of the theory of global, small, smooth solutions to initial value problems for non linear evolution equa tions. The addressed audience included graduate students of both mathematics and physics who were only assumed to have abasie knowledge of linear partial differential equations. Thus, in the spirit of the underlying series, this book is intended to serve as a detailed basis for lectures on the subject as weIl as for self-studies for students or for other newcomers to this field. The presentation of the theory is made using the classical method of continuation of local solutions with the help of apriori estimates obtained for small data. The corre sponding global existence theorems have been proved mainly in the last decade, focussing on fully nonlinear systems; Related questions concerning large data problems, the ex istence of weak solutions or the analysis of &.hock waves are not discussed. Also the question of optimal regularity assumptions on the coefficients is beyond the scope of the book and is touched only in part and exemplarily.
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Manifolds And Modular Forms

by Friedrich Hirzebruch, Rainer Jung e Thomas Berger

59,61€ + 10% CARD

 During the winter term 1987/88 I gave a course at the University of Bonn under the title "Manifolds and Modular Forms". I wanted to develop the theory of "Elliptic Genera" and to learn it myself on this occasion. This theory due to Ochanine, Landweber, Stong and others was relatively new at the time. The word "genus" is meant in the sense of my book "Neue Topologische Methoden in der Algebraischen Geometrie" published in 1956: A genus is a homomorphism of the Thorn cobordism ring of oriented compact manifolds into the complex numbers. Fundamental examples are the signature and the A-genus. The A-genus equals the arithmetic genus of an algebraic manifold, provided the first Chern class of the manifold vanishes. According to Atiyah and Singer it is the index of the Dirac operator on a compact Riemannian manifold with spin structure. The elliptic genera depend on a parameter. For special values of the parameter one obtains the signature and the A-genus. Indeed, the universal elliptic genus can be regarded as a modular form with respect to the subgroup r (2) of the modular group; the two cusps 0 giving the signature and the A-genus. Witten and other physicists have given motivations for the elliptic genus by theoretical physics using the free loop space of a manifold.
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Noncommutative Geometry And Number Theory - Where Arithmetic Meets Geometry And Physics

79,49€ + 10% CARD

 In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. Research across these ?elds has now reached an imp- tant turning point, as shows the increasing interest with which the mathematical community approaches these topics. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new c- nections between the ?elds of number theory, algebraic geometry and noncom- tative geometry. Thecontributionstothisvolumepartlyre?ectthetwoworkshops"Noncom- tative Geometry and Number Theory" that took place at the Max-Planck-Institut f¨ ur Mathematik in Bonn, in August 2003 and June 2004. The two workshops were the ?rst activity entirely dedicated to the interplay between these two ?elds of mathematics. An important part of the activities, which is also re?ected in this volume, came from the hindsight of physics which often provides new perspectives onnumber theoretic problems that make it possible to employ the tools of nonc- mutative geometry, well designed to describe the quantum world.
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Lectures On Algebraic Geometry Ii - Basic Concepts, Coherent Cohomology, Curves And Their Jacobians

by Gunter Harder

171,59€ + 10% CARD

 This second volume introduces the concept of shemes, reviews some commutative algebra and introduces projective schemes.
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Lectures On Algebraic Geometry I - Sheaves, Cohomology Of Sheaves, And Applications To Riemann Surfaces

by Gunter Harder

145,09€ + 10% CARD

 This book and the following second volume is an introduction into modern algebraic geometry.
ENGLISH

Lectures On Algebraic Geometry I - Sheaves, Cohomology Of Sheaves, And Applications To Riemann Surfaces

by Gunter Harder

63,59€ + 10% CARD

 This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own.In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them.
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Deformation Spaces - Perspectives On Algebro-Geometric Moduli

by Hossein Abbaspour, Matilde Marcolli e Thomas Tradler

59,61€ + 10% CARD

 The first instances of deformation theory were given by Kodaira and Spencer for complex structures and by Gerstenhaber for associative algebras. Since then, deformation theory has been applied as a useful tool in the study of many other mathematical structures, and even today it plays an important role in many developments of modern mathematics.This volume collects a few self-contained and peer-reviewed papers by experts which present up-to-date research topics in algebraic and motivic topology, quantum field theory, algebraic geometry, noncommutative geometry and the deformation theory of Poisson algebras. They originate from activities at the Max-Planck-Institute for Mathematics and the Hausdorff Center for Mathematics in Bonn.
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Quantum Groups And Noncommutative Spaces - Perspectives On Quantum Geometry

52,99€ + 10% CARD

 This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic representation, theoretic, analytic, and differential-geometric approaches. It also covers recent developments in Noncommutative Geometry, which have close relations to quantization and quantum group symmetries. The volume collects surveys by experts which originate from an acitvity at the Max-Planck-Institute for Mathematics in Bonn.
ENGLISH

Lectures On Algebraic Geometry I - Sheaves, Cohomology Of Sheaves, And Applications To Riemann Surfaces

by Gunter Harder

115,59€ + 10% CARD

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 This book and the following second volume is an introduction into modern algebraic geometry.
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