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Algebraic Geometry III Complex Algebraic Varieties Algebraic Curves and Their Jacobians

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...

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Bibliographic Details
Other Authors: Parshin, A.N. (Editor), Shafarevich, I.R. (Editor)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1998, 1998
Edition:1st ed. 1998
Series:Encyclopaedia of Mathematical Sciences
Subjects:
Number Theory
Algebraic Geometry
Mathematical Analysis
Analysis
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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520 |a 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 

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