Hyperelliptic surfaces are Loewner
Differential Geometry
2007-05-23 v2 Algebraic Geometry
Complex Variables
Abstract
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.
Keywords
Cite
@article{arxiv.math/0407009,
title = {Hyperelliptic surfaces are Loewner},
author = {Mikhail G. Katz and Stephane Sabourau},
journal= {arXiv preprint arXiv:math/0407009},
year = {2007}
}
Comments
9 pages. Proceedings Amer. Math. Soc., to appear