Elliptic curves of bounded degree in a polarized Abelian variety

DOI10.13137/2464-8728/27068zbMATH Open1440.14209arXiv1306.2007MaRDI QIDQ3297888

Lucio Guerra

Publication date: 21 July 2020

Abstract: For a polarized complex Abelian variety A, of dimension g>1, we study the function N_A(t) counting the number of elliptic curves in A with degree bounded by t. We describe elliptic curves as solutions of Diophantine equations which, at least for small dimensions g=2 and g=3, can actually be made explicit, and we show that computing the number of solutions is reduced to the classical topic in Number Theory of counting points of the lattice Z^n lying on an explicit bounded subset of R^n. We obtain, for Abelian varieties of small dimension, some upper bounds for the counting function.

Full work available at URL: https://arxiv.org/abs/1306.2007

zbMATH Keywords

abelian varietypolarizationelliptic curve

Mathematics Subject Classification ID

Elliptic curves (14H52) Analytic theory of abelian varieties; abelian integrals and differentials (14K20)

Related Items (1)

Polynomial bounds for Arakelov invariants of Belyi curves. With an appendix by Peter Bruin.

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