任意约化群Hitchin系统阿贝尔化的初等方法
alg-geom
2008-02-03 v3 代数几何
摘要
我们考虑紧Riemann曲面C（亏格>1）上稳定主G-丛的模空间，其中G是约化代数群。我们显式构造了一个从Hitchin映射的通用纤维到与C的某个适当Galois覆盖相关联的广义Prym簇的映射F。映射F具有有限纤维。在G=PGl(2)的情形，可以验证F的通用纤维是相对于个副本的乘积的主齐性空间，其中d是C上典范丛的次数。然而，当G的Dynkin图不包含（n>0）型分支，或换位子子群(G,G)是单连通时，映射F是单射。
引用
@article{arxiv.alg-geom/9412020,
title = {An elementary approach to the abelianization of the Hitchin system for arbitrary reductive groups},
author = {R. Scognamillo},
journal= {arXiv preprint arXiv:alg-geom/9412020},
year = {2008}
}
备注
25 pages, LaTex. In the revised version, the most relevant changes are in the proofs contained in section 3. The major ones concern the proof of theorem 3.2 (theorem 3.1 in the revised version)