Definability of restricted theta functions and families of abelian varieties

Ya'acov Peterzil; Sergei Starchenko

doi:10.1215/00127094-2080018

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arXiv · 1103.3110

Definability of restricted theta functions and families of abelian varieties

Ya'acov Peterzil·Sergei Starchenko

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Abstract

We consider some classical maps from the theory of abelian varieties and their moduli spaces and prove their definability, on restricted domains, in the o-minimal structure $\Rae$. In particular, we prove that the embedding of moduli space of principally polarized ableian varierty, $Sp(2g,\Z)\backslash \CH_g$, is definable in $\Rae$, when restricted to Siegel's fundamental set $\fF_g$. We also prove the definability, on appropriate domains, of embeddings of families of abelian varieties into projective space.

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Ya'acov Peterzil, Sergei Starchenko. 2011-03-16. Definability of restricted theta functions and families of abelian varieties. https://doi.org/10.1215/00127094-2080018

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