33 research outputs found
Definability of restricted theta functions and families of abelian varieties
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