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Mathematics - Algebra | Algebraic Geometry III - Complex Algebraic Varieties Algebraic Curves and Their Jacobians

Algebraic Geometry III

Complex Algebraic Varieties Algebraic Curves and Their Jacobians

Parshin, A.N., Shafarevich, I.R. (Eds.)

Translated by Rivin, I.

Original Russian edition published by VINITI, Moscow, 1989

1998, VIII, 270 p.

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  • About this book

The first contribution of this EMS volume on the subject of complex algebraic geometry touches upon many of the central problems in this vast and very active area of current research. While it is much too short to provide complete coverage of this subject, it provides a succinct summary of the areas it covers, while providing in-depth coverage of certain very important fields - some examples of the fields treated in greater detail are theorems of Torelli type, K3 surfaces, variation of Hodge structures and degenerations of algebraic varieties.
The second part provides a brief and lucid introduction to the recent work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieties, and partial differential equations of mathematical physics. The paper discusses the work of Mumford, Novikov, Krichever, and Shiota, and would be an excellent companion to the older classics on the subject by Mumford.

Content Level » Research

Keywords » Algebraic curves - Complex algebraic varieties - Hodge structures - Hodgesche Struktur - Jacobian varieties - Jacobischen Varietät - Sätze von - algebraic varieties - algebraische Kurven - differential equation - komplexe algebraische Varietät - mathematical physics

Related subjects » Algebra - Analysis - Number Theory and Discrete Mathematics

Table of contents 

I. Complex Algebraic Varieties: Periods of Integrals and Hodge Structures.- II. Algebraic Curves and Their Jacobians.

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