PreprintCC BY 4.0arXiv
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.
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BibTeX
@misc{brosnan2026discriminants,
title = {{Discriminants of Hermitian forms, maximal degenerations and Kontsevich's tropical approach to the Hodge conjecture}},
author = {Patrick Brosnan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14169},
eprint = {2609.14169},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14169},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Discriminants of Hermitian forms, maximal degenerations and Kontsevich's tropical approach to the Hodge conjecture
AU - Patrick Brosnan
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.14169
UR - https://arxiv.org/abs/2609.14169
AB - 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.
ER -