Effective reconstruction of curves from their theta hyperplanes

Details Effective reconstruction of curves from their theta hyperplanes Effective reconstruction of curves from their theta hyperplanes

2010-01-08

arxiv.org/abs/1001.1237v2

Mathematics

Algebraic Geometry

10 pages, corrected typos, and corrected 1.1

Scientific paper

Working over the complex numbers, and considering a generic curve C of genus g>3 and a non-trivial 2-torsion point alpha on it's Jacobian JC, we give a new interpretation of Mumfords map -- chi : H^0(JC, Theta_C+t_alpha Tehta_C) -> H^0(Prym(C,alpha), 2Theta_{Prym(C,alpha)}). -- We use this interpretation to effectively reconstruct C from its odd theta hyperplanes; hence we also get an effective generic-inverse for the Torelli map.

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