2003/10/07 by Samuel Grushevsky, Grushevsky, Samuel, Riccardo Salvati Manni +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.math/0310085
arxiv created 2003/10/07 · arxiv updated 2009/12/01
We show that a generic principally polarized abelian variety (ppav) is uniquely determined by its theta hyperplanes. These are the non-projectivized version of those studied by Caporaso and Sernesi (see math.AG/0204164), which in a sense are a generalization to ppavs of bitangents of plane quartics, and of hyperplanes tangent to a canonical curves of genus g in g-1 points. More precisely, we show that, generically, the set of gradients of all odd theta functions at the point zero uniquely determines a ppav with level (4,8) structure. We also show that our map is an immersion of the moduli space of ppavs.