Subspaces of moduli spaces of rank one local systems
Subspaces of moduli spaces of rank one local systems
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一阶局部系统模空间的子空间
DOI：
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发表时间：
1993
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通讯作者：
C. Simpson
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作者：
C. Simpson
。-设X是光滑投射簇。X上一阶局部系统的模空间M(X)具有三种不同的复代数群结构(Betti、de Rham和Dolbeault)。对所有三种结构都是代数的子群，我们称其为三重环面。我们证明了M(X)的任一闭子空间S是三重环面的平移与扭点的有限并，它是以自然方式定义的，例如通过上同调群及其相关构造。这回答了波维尔和卡塔尼斯人的一个猜想。证明平移是由扭点决定的，这是基于超越数论的一个结果。
. - Suppose X is a smooth projective variety. The moduli space M (X) of rank one local systems on X has three different structures of complex algebraic group (Betti, de Rham, and Dolbeault). A subgroup which is algebraic for all three structures, we call a triple torus. We show that any closed subspace S of M (X) which is defined in a natural way, for example by looking at cohomology groups and related constructions, is a finite union of translates of triple tori by torsion points. This answers a conjecture of Beauville and Catanese. The proof that the translates are by torsion points rests on a result from transcendental number theory.