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Author: Alexander Polishchuk
Publisher: Cambridge University Press
Published: 2003-04-21
Total Pages: 308
ISBN-13: 0521808049
DOWNLOAD EBOOKPresents a modern treatment of the theory of theta functions in the context of algebraic geometry.
Author: Louis Auslander
Publisher: American Mathematical Soc.
Published: 1977
Total Pages: 106
ISBN-13: 0821816845
DOWNLOAD EBOOKConsists of three chapters covering the following topics: foundations, bilinear forms and presentations of certain 2-step nilpotent Lie groups, discrete subgroups of the Heisenberg group, the automorphism group of the Heisenberg group, fundamental unitary representations of the Heisenberg group, and the Fourier transform and the Weil-Brezin map.
Author: Jonathan M. Fraser
Publisher: Cambridge University Press
Published: 2020-10-29
Total Pages: 287
ISBN-13: 1108478654
DOWNLOAD EBOOKThe first thorough treatment of the Assouad dimension in fractal geometry, with applications to many fields within pure mathematics.
Author: Christina Birkenhake
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 635
ISBN-13: 3662063077
DOWNLOAD EBOOKThis book explores the theory of abelian varieties over the field of complex numbers, explaining both classic and recent results in modern language. The second edition adds five chapters on recent results including automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture. ". . . far more readable than most . . . it is also much more complete." Olivier Debarre in Mathematical Reviews, 1994.
Author: Jaques Calmet
Publisher: Springer Science & Business Media
Published: 1986-07
Total Pages: 430
ISBN-13: 9783540167761
DOWNLOAD EBOOKAuthor: Herbert Lange
Publisher: Springer Nature
Published: 2023-03-15
Total Pages: 390
ISBN-13: 3031255704
DOWNLOAD EBOOKThis textbook offers an introduction to abelian varieties, a rich topic of central importance to algebraic geometry. The emphasis is on geometric constructions over the complex numbers, notably the construction of important classes of abelian varieties and their algebraic cycles. The book begins with complex tori and their line bundles (theta functions), naturally leading to the definition of abelian varieties. After establishing basic properties, the moduli space of abelian varieties is introduced and studied. The next chapters are devoted to the study of the main examples of abelian varieties: Jacobian varieties, abelian surfaces, Albanese and Picard varieties, Prym varieties, and intermediate Jacobians. Subsequently, the Fourier–Mukai transform is introduced and applied to the study of sheaves, and results on Chow groups and the Hodge conjecture are obtained. This book is suitable for use as the main text for a first course on abelian varieties, for instance as a second graduate course in algebraic geometry. The variety of topics and abundant exercises also make it well suited to reading courses. The book provides an accessible reference, not only for students specializing in algebraic geometry but also in related subjects such as number theory, cryptography, mathematical physics, and integrable systems.
Author: Jay Jorgenson
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 410
ISBN-13: 0821836986
DOWNLOAD EBOOKThe aim of this volume is to bring together research ideas from various fields of mathematics which utilize the heat kernel or heat kernel techniques in their research. The intention of this collection of papers is to broaden productive communication across mathematical sub-disciplines and to provide a vehicle which would allow experts in one field to initiate research with individuals in another field, as well as to give non-experts a resource which can facilitate expanding theirresearch and connecting with others.
Author: Daniel Huybrechts
Publisher: Clarendon Press
Published: 2006-04-20
Total Pages: 316
ISBN-13: 019151635X
DOWNLOAD EBOOKThis seminal text on Fourier-Mukai Transforms in Algebraic Geometry by a leading researcher and expositor is based on a course given at the Institut de Mathematiques de Jussieu in 2004 and 2005. Aimed at postgraduate students with a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. Including notions from other areas, e.g. singular cohomology, Hodge theory, abelian varieties, K3 surfaces; full proofs are given and exercises aid the reader throughout.
Author: Eberhard Freitag
Publisher: Springer Science & Business Media
Published: 2011-06-10
Total Pages: 521
ISBN-13: 3642205542
DOWNLOAD EBOOKThe book contains a complete self-contained introduction to highlights of classical complex analysis. New proofs and some new results are included. All needed notions are developed within the book: with the exception of some basic facts which can be found in the ̄rst volume. There is no comparable treatment in the literature.
Author: David Mumford
Publisher: Springer Science & Business Media
Published: 2007-06-25
Total Pages: 248
ISBN-13: 0817645772
DOWNLOAD EBOOKThis volume is the first of three in a series surveying the theory of theta functions. Based on lectures given by the author at the Tata Institute of Fundamental Research in Bombay, these volumes constitute a systematic exposition of theta functions, beginning with their historical roots as analytic functions in one variable (Volume I), touching on some of the beautiful ways they can be used to describe moduli spaces (Volume II), and culminating in a methodical comparison of theta functions in analysis, algebraic geometry, and representation theory (Volume III).
