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Preprint Number 308

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308. Ya'acov Peterzil and Sergei Starchenko
Definability of restricted theta functions and families of abelian varieties

Submission date: 16 March 2011.


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 R_{an,exp}. In particular, we prove that the embedding of moduli space of principally polarized ableian varierty, Sp(2g,Z)\H_g, is definable in R_{an,exp}, when restricted to Siegel's fundamental set F_g. We also prove the defiability, on appropriate domains, of embeddings of families of abelian varieties into projective space.

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