Algebraic Geometry III
Subtitle: Complex Algebraic Varieties Algebraic Curves and Their Jacobians
By: by Viktor S. Kulikov, P. F. Kurchanov, V. V. Shokurov ; edited by A. N. Parshin, I. R. Shafarevich
Contributors: Kurchanov, P. F.; Shokurov, V. V.; Parshin, A. N.; Shafarevich, I. R.
Series: Encyclopaedia of Mathematical Sciences -- 36; Encyclopaedia of Mathematical Sciences -- 36
Publisher: Springer Berlin Heidelberg
Published: 1998
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] :
Number of pages: 270
ISBN-13: 9783642081187; 9783662036624
Subjects: Geometry, algebraic; Mathematics; Global analysis (Mathematics); Number theory
Description: 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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