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

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.