Vector bundles on curves and generalized theta functions: recent results and open problems
Vector bundles on curves and generalized theta functions: recent results and open problems
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发表时间：
1994-04
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通讯作者：
Arnaud Beauville
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作者：
Arnaud Beauville
紧黎曼曲面上向量丛的模空间带有一个自然线丛，即行列式丛。这个线丛的截面和它的倍数构成了经典θ函数的非阿贝尔推广。来自数学物理学的新思想为这些截面的空间提供了新的视角，特别是允许计算它们的尺寸（Verlinde公式）。这篇综述论文致力于概述这些想法和关于这个问题的最重要的最近结果。
The moduli spaces of vector bundles on a compact Riemann surface carry a natural line bundle, the determinant bundle. The sections of this line bundle and its multiples constitute a non-abelian generalization of the classical theta functions. New ideas coming from mathematical physics have shed a new light on these spaces of sections—allowing notably to compute their dimension (Verlinde’s formula). This survey paper is devoted to giving an overview of these ideas and of the most important recent results on the subject.