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arXiv · 2609.14169

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

Patrick Brosnan
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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.

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Patrick Brosnan. 2026-09-12. Discriminants of Hermitian forms, maximal degenerations and Kontsevich's tropical approach to the Hodge conjecture. https://arxiv.org/abs/2609.14169

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