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On elliptic curves of bounded degree in a polarized Abelian variety
Guerra, Lucio
2019
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e-ISSN
2464-8728
Abstract
For a polarized complex Abelian variety $A$ we study the function $N_A(t)$
counting the number of elliptic curves in $A$ with degree bounded by $t$.
This extends our previous work in dimension two.
We describe the collection of elliptic curves in the product $A = S \times F$ of an
Abelian variety and an elliptic curve by means of an explicit parametrization, and
in terms of the parametrization we express the degrees of elliptic curves
relative to a split polarization.
When this is applied to the self product $A = E^k$ of an elliptic curve,
it turns out that an asymptotic estimate of the counting function $N_A(t)$ can
be obtained from an asymptotic study of the degree form on the group of endomorphisms of the elliptic curve.
Publisher
EUT Edizioni Università di Trieste
Source
Lucio Guerra, "On elliptic curves of bounded degree in a polarized Abelian variety", in: "Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol. 51 (2019)", Trieste, EUT Edizioni Università di Trieste, 2019, pp. 105-123
Languages
en
Rights
Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
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