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 curve; Abelian variety; polarization 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 anAbelian variety and an elliptic curve by means of an explicit parametrization, andin 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 $N_A(t)$ canbe 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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