Discriminants of Hermitian forms, maximal degenerations and Kontsevich's tropical approach to the Hodge conjecture

Abstract

Motivated by Markman's work and by Kontsevich's tropical approach to disproving the Hodge conjecture, this note explains why families of Weil type abelian 2n-folds only have maximal unipotent degeneration when the discriminant is $(-1{)}^n$. Along the way, it explains what the discriminant is and collects various facts about Weil type abelian varieties.