87 research outputs found

    Definability of restricted theta functions and families of abelian varieties

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    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

    Uniform bounds on growth in o-minimal structures

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    We prove that a function definable with parameters in an o-minimal structure is bounded away from infinity as its argument goes to infinity by a function definable without parameters, and that this new function can be chosen independently of the parameters in the original function. This generalizes a result in a paper of Friedman and Miller. Moreover, this remains true if the argument is taken to approach any element of the structure (or plus/minus infinity), and the function has limit any element of the structure (or plus/minus infinity).Comment: 3 pages. To appear in Mathematical Logic Quarterl