Definability of restricted theta functions and families of abelian varieties

2013/03/15 by Ya’acov Peterzil, Sergei Starchenko · 1 citation
Mathematics · #Advanced Topology and Set Theory #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory

paper · pdf · doi:10.1215/00127094-2080018

openalex publication_date 2013/03/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Mild manifolds and a non-standard Riemann existence theorem
• Geometric categories and o-minimal structures
• On the real exponential field with restricted analytic functions
• Uniform definability of the Weierstrass \wp functions and generalized tori of dimension one

Cited by

• Sergei Starchenko [wikipedia]