[书籍] 代数曲线几何（第2卷 第2分册）
出版社:
世界图书出版公司
简介:
This volume is devoted to the foundations of the theory of moduli of algebraic curves defined over the complex numbers. The first volume was almost exclusively concerned with the geometry on a fixed, smooth curve. At the time it was published, the local deformation theory of a smooth curve was well understood, but the study of the geometry of global moduli was in its early stages. This study has since undergone explosive development and continues to do so. There are two reasons for this; one predictable at the time of the first volume, the other not. The predictable one was the intrinsic algebro-geometric interest in the moduli of curves; this has certainly turned out to be the case. The other is the external influence from physics. Because of this confluence, the subject has developed in ways that are incredibly richer than could have been imagined at the time of writing of Volume I. When this volume, GAC II, was planned it was envisioned that the cen- terpiece would be the study of linear series on a general or variable curve, culminating in a proof of the Petri conjecture. This is still an important part of the present volume, but it is not the central aspect. Rather, the main purpose of the book is to provide comprehensive and detailed foundations for the theory of the moduli of algebraic curves. In addition, we feel that a very important, perhaps distinguishing, aspect of GAC II is the blending of the multiple perspectives-algebro-geometric, complex-analytic, topological, and combinatorial-that are used for the study of the moduli of curves.
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