arXiv math/04070092004-07math.DGmath.AGmath.CV

Hyperelliptic surfaces are Loewner

Mikhail G. Katz, Stephane Sabourau

备注：: 9 pages. Proceedings Amer. Math. Soc., to appear

英文摘要：

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.

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