Duke Mathematical Journal

Definability of restricted theta functions and families of abelian varieties

Ya’acov Peterzil and Sergei Starchenko

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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.

Article information

Source
Duke Math. J., Volume 162, Number 4 (2013), 731-765.

Dates
First available in Project Euclid: 15 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1363355692

Digital Object Identifier
doi:10.1215/00127094-2080018

Mathematical Reviews number (MathSciNet)
MR3039679

Zentralblatt MATH identifier
1284.03215

Subjects
Primary: 03C64: Model theory of ordered structures; o-minimality 03C98: Applications of model theory [See also 03C60] 14K25: Theta functions [See also 14H42] 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
Secondary: 14G35: Modular and Shimura varieties [See also 11F41, 11F46, 11G18] 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35]

Citation

Peterzil, Ya’acov; Starchenko, Sergei. Definability of restricted theta functions and families of abelian varieties. Duke Math. J. 162 (2013), no. 4, 731--765. doi:10.1215/00127094-2080018. https://projecteuclid.org/euclid.dmj/1363355692


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