Share

Complex Tori and Abelian Varieties

2005 Mathematics
Download Complex Tori and Abelian Varieties PDF Online Free

Author :
Release : 2005
Genre : Mathematics
Kind : eBook
Book Rating : 656/5 ( reviews)

GET EBOOK


Book Synopsis Complex Tori and Abelian Varieties by : Olivier Debarre

Download or read book Complex Tori and Abelian Varieties written by Olivier Debarre. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Complex Abelian Varieties

2013-03-09 Mathematics
Download Complex Abelian Varieties PDF Online Free

Author :
Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 887/5 ( reviews)

GET EBOOK


Book Synopsis Complex Abelian Varieties by : Herbert Lange

Download or read book Complex Abelian Varieties written by Herbert Lange. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Complex Tori

2012-12-06 Mathematics
Download Complex Tori PDF Online Free

Author :
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 668/5 ( reviews)

GET EBOOK


Book Synopsis Complex Tori by : Herbert Lange

Download or read book Complex Tori written by Herbert Lange. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: A complex torus is a connected compact complex Lie group. Any complex 9 9 torus is of the form X =

Abelian Varieties, Theta Functions and the Fourier Transform

2003-04-21 Mathematics
Download Abelian Varieties, Theta Functions and the Fourier Transform PDF Online Free

Author :
Release : 2003-04-21
Genre : Mathematics
Kind : eBook
Book Rating : 049/5 ( reviews)

GET EBOOK


Book Synopsis Abelian Varieties, Theta Functions and the Fourier Transform by : Alexander Polishchuk

Download or read book Abelian Varieties, Theta Functions and the Fourier Transform written by Alexander Polishchuk. This book was released on 2003-04-21. Available in PDF, EPUB and Kindle. Book excerpt: Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.

Complex Abelian Varieties and Theta Functions

2012-12-06 Mathematics
Download Complex Abelian Varieties and Theta Functions PDF Online Free

Author :
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 791/5 ( reviews)

GET EBOOK


Book Synopsis Complex Abelian Varieties and Theta Functions by : George R. Kempf

Download or read book Complex Abelian Varieties and Theta Functions written by George R. Kempf. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

You may also like...