PreprintCC BY 4.0arXiv
Tropical Regularity
Abstract
We introduce the notion of tropical regularity as a generalization of tropical smoothness and present a geometric classification conjecture for tropical regular cycles. Roughly, the conjecture predicts that every regular tuple either forms a regular fibration or descends via a lattice projection to one of finitely many minimal-model cycles. Our main results establish this conjecture in three fundamental cases:unmixed regular tuples (T,…,T,[F]) with L(T)={0} and [F] spanning its ambient space; regular tropicalizations of complete intersections with generic coefficients; and regular tropical $2$-cycles satisfying the Hodge index inequality and spanning their ambient space.
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BibTeX
@misc{li2026tropical,
title = {{Tropical Regularity}},
author = {Linxuan Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.24339},
eprint = {2606.24339},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.24339},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Tropical Regularity
AU - Linxuan Li
PY - 2026
DA - 2026/10/31
PB - arXiv
DO - 10.48550/arxiv.2606.24339
UR - https://arxiv.org/abs/2606.24339
AB - We introduce the notion of tropical regularity as a generalization of tropical smoothness and present a geometric classification conjecture for tropical regular cycles. Roughly, the conjecture predicts that every regular tuple either forms a regular fibration or descends via a lattice projection to one of finitely many minimal-model cycles. Our main results establish this conjecture in three fundamental cases:unmixed regular tuples (T,…,T,[F]) with L(T)={0} and [F] spanning its ambient space; regular tropicalizations of complete intersections with generic coefficients; and regular tropical $2$-cycles satisfying the Hodge index inequality and spanning their ambient space.
ER -