全纯二次微分间的线性关系与M_g上诱导的Siegel度量
代数几何
2011-10-26 v3 高能物理 - 理论
摘要
对亏格g大于3的典型曲线，我们导出了全纯abel微分的一组基中微分对乘积之间(g-2)(g-3)/2个线性无关关系的显式形式。结果表明Petri关系显著地吻合于行列式条件。我们仅用周期Riemann矩阵显式表达了由Siegel度量在典型曲线模空间M_g上诱导的体积形式。借助Kodaira-Spencer映射，这些关系导出了M_g上诱导Siegel度量的一个表达式，它对应于Bergman再生核的平方。起关键作用的是全纯微分的一组特异基，其性质也导致了Fay的三割线恒等式的直接推导。
引用
@article{arxiv.math/0506550,
title = {Linear relations among holomorphic quadratic differentials and induced Siegel's metric on M_g},
author = {Marco Matone and Roberto Volpato},
journal= {arXiv preprint arXiv:math/0506550},
year = {2011}
}
备注
10 pages - The Siegel induced volume form on M_g is expressed in terms of the Riemann period matrix only, it is simply related to the Bergman reproducing kernel. Bases of holomorphic n-differentials are introduced, whose distinguished properties also lead to an immediate derivation of Fay's trisecant identity