Hyperelliptic surfaces are Loewner
微分几何
2007-05-23 v2 代数几何
复变函数
摘要
We prove that C. Loewner's inequality for the torus is satisfied by all hyperelliptic surfaces X, as well. We first construct the Loewner loops on the (mildly singular) companion tori, locally isometric to X away from the Weierstrass points. The loops are then transplanted to X, and surgered to obtain a Loewner loop on X. In higher genus, we exploit M. Gromov's area estimates for epsilon-regular metrics on X.
引用
@article{arxiv.math/0407009,
title = {Hyperelliptic surfaces are Loewner},
author = {Mikhail G. Katz and Stephane Sabourau},
journal= {arXiv preprint arXiv:math/0407009},
year = {2007}
}
备注
9 pages. Proceedings Amer. Math. Soc., to appear