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15 March 2013 Definability of restricted theta functions and families of abelian varieties
Ya’acov Peterzil, Sergei Starchenko
Duke Math. J. 162(4): 731-765 (15 March 2013). DOI: 10.1215/00127094-2080018

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.

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Ya’acov Peterzil. Sergei Starchenko. "Definability of restricted theta functions and families of abelian varieties." Duke Math. J. 162 (4) 731 - 765, 15 March 2013. https://doi.org/10.1215/00127094-2080018

Information

Published: 15 March 2013
First available in Project Euclid: 15 March 2013

zbMATH: 1284.03215
MathSciNet: MR3039679
Digital Object Identifier: 10.1215/00127094-2080018

Subjects:
Primary: 03C64, 03C98, 11F46, 14K25
Secondary: 11G18, 14G35

Rights: Copyright © 2013 Duke University Press

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Vol.162 • No. 4 • 15 March 2013
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