Abelian varieties with group action
代数几何
2007-05-23 v2
摘要
Let G be a finite group acting on a smooth projective curve X. This induces an action of G on the Jacobian JX of X and thus a decomposition of JX up to isogeny. The most prominent example of such a situation is the group G of two elements. Let X --> Y denote the corresponding quotient map. Then JX is isogenous to the product of JY with the Prym variety of X/Y. In this paper some general results on group actions on abelian varieties are given and applied to deduce a decomposition of the jacobian JX for arbitrary group actions. Several examples are given.
引用
@article{arxiv.math/0106055,
title = {Abelian varieties with group action},
author = {H. Lange and S. Recillas},
journal= {arXiv preprint arXiv:math/0106055},
year = {2007}
}
备注
30 pages, corrected version abbriviated to 21 pages, to appear in Journ. Reine Angew. Mathem