Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/27068
Title: On elliptic curves of bounded degree in a polarized Abelian variety
Authors: Guerra, Lucio
Keywords: Elliptic curveAbelian varietypolarization
Issue Date: 2019
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
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.
Type: Article
URI: http://hdl.handle.net/10077/27068
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/2464-8728/27068
Rights: Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Appears in Collections:Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.51 (2019)

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