Vari\'et\'es ab\'eliennes et th\'eor\`eme de Minkowski-Hlawka

TL;DR

This paper improves the known lower bounds on lattice packing densities in the context of complex abelian varieties, extending classical Minkowski-Hlawka results and confirming Muetzel's conjecture.

Contribution

It provides an enhanced version of the Minkowski-Hlawka theorem for complex abelian varieties, advancing the understanding of lattice packings in complex geometry.

Findings

Improved lower bounds for lattice packing densities in complex abelian varieties

Confirmation of Muetzel's conjecture in this context

Extension of classical Minkowski-Hlawka theorem to complex settings

Abstract

A classical theorem of Minkowski and Hlawka states that there exists a lattice in R^n with packing density at least 2^{1-n}. Buser and Sarnak proved the analogue of this result in the context of complex abelian varieties. Here we give an improvement of this analogue; this shows a conjecture of Muetzel.