Analytic Theory Of Abelian Varieties
DOWNLOAD
Download Analytic Theory Of Abelian Varieties PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Analytic Theory Of Abelian Varieties book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Analytic Theory Of Abelian Varieties
DOWNLOAD
Author : H. P. F. Swinnerton-Dyer
language : en
Publisher: Cambridge University Press
Release Date : 1974-12-12
Analytic Theory Of Abelian Varieties written by H. P. F. Swinnerton-Dyer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-12-12 with Mathematics categories.
The study of abelian manifolds forms a natural generalization of the theory of elliptic functions, that is, of doubly periodic functions of one complex variable. When an abelian manifold is embedded in a projective space it is termed an abelian variety in an algebraic geometrical sense. This introduction presupposes little more than a basic course in complex variables. The notes contain all the material on abelian manifolds needed for application to geometry and number theory, although they do not contain an exposition of either application. Some geometrical results are included however.
Analytic Theory Of Abelian Varieties
DOWNLOAD
Author : H. P. F. Swinnerton-Dyer
language : en
Publisher:
Release Date : 1974
Analytic Theory Of Abelian Varieties written by H. P. F. Swinnerton-Dyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Abelian varieties categories.
This introduction presupposes little more than a basic course in complex variables.
Introduction To Abelian Varieties
DOWNLOAD
Author : Vijaya Kumar Murty
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Introduction To Abelian Varieties written by Vijaya Kumar Murty and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Abelian varieties categories.
This book presents an elementary and self-contained approach to Abelian varieties, a subject that plays a central role in algebraic and analytic geometry, number theory, and complex analysis. The book is based on notes from a course given at Concordia University and would be useful for independent study or as a textbook for graduate courses in complex analysis, Riemann surfaces, number theory, or analytic geometry. Murty works mostly over the complex numbers, discussing the theorem of Abel-Jacobi and Lefschetz's theorem on projective embeddings. After presenting some examples, Murty touches on Abelian varieties over number fields, as well as the conjecture of Tate (Faltings's theorem) and its relation to Mordell's conjecture. References are provided to guide the reader in further study.
Complex Abelian Varieties And Theta Functions
DOWNLOAD
Author : George R. Kempf
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Complex Abelian Varieties And Theta Functions written by George R. Kempf and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Abelian varieties are a natural generalization of elliptic curves to higher dimensions, whose geometry and classification are as rich in elegant results as in the one-dimensional ease. The use of theta functions, particularly since Mumford's work, has been an important tool in the study of abelian varieties and invertible sheaves on them. Also, abelian varieties play a significant role in the geometric approach to modern algebraic number theory. In this book, Kempf has focused on the analytic aspects of the geometry of abelian varieties, rather than taking the alternative algebraic or arithmetic points of view. His purpose is to provide an introduction to complex analytic geometry. Thus, he uses Hermitian geometry as much as possible. One distinguishing feature of Kempf's presentation is the systematic use of Mumford's theta group. This allows him to give precise results about the projective ideal of an abelian variety. In its detailed discussion of the cohomology of invertible sheaves, the book incorporates material previously found only in research articles. Also, several examples where abelian varieties arise in various branches of geometry are given as a conclusion of the book.
Complex Tori And Abelian Varieties
DOWNLOAD
Author : Olivier Debarre
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Complex Tori And Abelian Varieties written by Olivier Debarre and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This graduate-level textbook introduces the classical theory of complex tori and abelian varieties, while presenting in parallel more modern aspects of complex algebraic and analytic geometry. Beginning with complex elliptic curves, the book moves on to the higher-dimensional case, giving characterizations from different points of view of those complex tori which are abelian varieties, i.e., those that can be holomorphically embedded in a projective space. This allows, on the one hand, for illuminating the computations of nineteenth-century mathematicians, and on the other, familiarizing readers with more recent theories. Complex tori are ideal in this respect: One can perform "hands-on" computations without the theory being totally trivial. Standard theorems about abelian varieties are proved, and moduli spaces are discussed. Recent results on the geometry and topology of some subvarieties of a complex torus are also included. The book contains numerous examples and exercises. It is a very good starting point for studying algebraic geometry, suitable for graduate students and researchers interested in algebra and algebraic geometry. Information for our distributors: SMF members are entitled to AMS member discounts.
Abelian Varieties
DOWNLOAD
Author : David Mumford
language : en
Publisher: Oxford University Press, USA
Release Date : 1970
Abelian Varieties written by David Mumford and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Language Arts & Disciplines categories.
Now back in print, the revised edition of this popular study gives a systematic account of the basic results about abelian varieties. Mumford describes the analytic methods and results applicable when the ground field k is the complex field C and discusses the scheme-theoretic methods and results used to deal with inseparable isogenies when the ground field k has characteristic p. The author also provides a self-contained proof of the existence of a dual abeilan variety, reviews the structure of the ring of endormorphisms, and includes in appendices "The Theorem of Tate" and the "Mordell-Weil Thorem." This is an established work by an eminent mathematician and the only book on this subject.
Complex Abelian Varieties
DOWNLOAD
Author : Herbert Lange
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Complex Abelian Varieties written by Herbert Lange and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Abelian varieties are special examples of projective varieties. As such theycan be described by a set of homogeneous polynomial equations. The theory ofabelian varieties originated in the beginning of the ninetheenth centrury with the work of Abel and Jacobi. The subject of this book is the theory of abelian varieties over the field of complex numbers, and it covers the main results of the theory, both classic and recent, in modern language. It is intended to give a comprehensive introduction to the field, but also to serve as a reference. The focal topics are the projective embeddings of an abelian variety, their equations and geometric properties. Moreover several moduli spaces of abelian varieties with additional structure are constructed. Some special results onJacobians and Prym varieties allow applications to the theory of algebraic curves. The main tools for the proofs are the theta group of a line bundle, introduced by Mumford, and the characteristics, to be associated to any nondegenerate line bundle. They are a direct generalization of the classical notion of characteristics of theta functions.
Introduction To The Classical Theory Of Abelian Functions
DOWNLOAD
Author : Alekse_ Ivanovich Markushevich
language : en
Publisher: American Mathematical Soc.
Release Date : 2006-07-26
Introduction To The Classical Theory Of Abelian Functions written by Alekse_ Ivanovich Markushevich and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-26 with Mathematics categories.
Historical introduction. The Jacobian inversion problem Periodic functions of several complex variables Riemann matrices. Jacobian (intermediate) functions Construction of Jacobian functions of a given type. Theta functions and Abelian functions. Abelian and Picard manifolds Appendix A. Skew-symmetric determinants Appendix B. Divisors of analytic functions Appendix C. A summary of the most important formulas
Abelian Varieties
DOWNLOAD
Author : Serge Lang
language : en
Publisher: Martino Fine Books
Release Date : 2014-04
Abelian Varieties written by Serge Lang and has been published by Martino Fine Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04 with Mathematics categories.
2014 Reprint of 1959 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. In mathematics, particularly in algebraic geometry, complex analysis and number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions. Abelian varieties are at the same time among the most studied objects in algebraic geometry and indispensable tools for much research on other topics in algebraic geometry and number theory. Serge Lang was a French-born American mathematician. He is known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He was a member of the Bourbaki group.
Abelian Varieties Theta Functions And The Fourier Transform
DOWNLOAD
Author : Alexander Polishchuk
language : en
Publisher: Cambridge University Press
Release Date : 2003-04-21
Abelian Varieties Theta Functions And The Fourier Transform written by Alexander Polishchuk and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-21 with Mathematics categories.
Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.