On Abelian subvarieties of bounded degree in a polarized Abelian variety

TL;DR

This paper investigates the growth rate of the number of Abelian subvarieties with bounded degree within a polarized Abelian variety, providing asymptotic estimates for their count.

Contribution

It introduces an estimate for the asymptotic growth of Abelian subvarieties with bounded Euler characteristic in a polarized Abelian variety.

Findings

Derived an asymptotic growth estimate for N_A(t)

Established bounds on the number of subvarieties with bounded degree

Provided insights into the distribution of Abelian subvarieties

Abstract

If A is an Abelian variety, endowed with a polarization L, we study the function N_A(t) which counts the number of Abelian subvarieties S in A such that for the induced polarization L|_S the Euler characteristic \chi(L|_S) is bounded above by t. We give an estimate for the asymptotic order of growth of this function.