PreprintarXiv licencearXiv
Numerical Kawamata--Viehweg vanishing for rank-three matroids
Abstract
We prove the numerical Kawamata--Viehweg conjecture for every matroid of rank three: the Euler characteristic of the inverse of an integral big and nef line bundle class is nonnegative. The proof reduces the conjecture to an inequality for a stone game.
Related
- Kawamata-Viehweg and Lipman's vanishings for sequences of blow-ups at regular closed points
- Counterexamples to the Ambro--Kawamata effective non-vanishing conjecture
- Orlik-Solomon algebras determine the Tutte polynomials of matroids of rank at most three
- Generic vanishing subschemes of codimension three
- Vanishing orders of Dirichlet solutions to the Schrödinger equation in dimensions three and higher
BibTeX
@misc{cheng2026numerical,
title = {{Numerical Kawamata--Viehweg vanishing for rank-three matroids}},
author = {Ronnie Cheng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41631},
eprint = {2610.41631},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41631},
}
RIS
TY - UNPB
TI - Numerical Kawamata--Viehweg vanishing for rank-three matroids
AU - Ronnie Cheng
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41631
UR - https://arxiv.org/abs/2610.41631
AB - We prove the numerical Kawamata--Viehweg conjecture for every matroid of rank three: the Euler characteristic of the inverse of an integral big and nef line bundle class is nonnegative. The proof reduces the conjecture to an inequality for a stone game.
ER -