Combinatorially equivalent hyperplane arrangements
Combinatorics
2021-04-05 v3 Algebraic Geometry
Abstract
We study the combinatorics of hyperplane arrangements over arbitrary fields. Specifically, we determine in which situation an arrangement and its reduction modulo a prime number have isomorphic lattices via the use of minimal strong -Gr\"obner bases. Moreover, we prove that the Terao's conjecture over finite fields implies the conjecture over the rationals.
Keywords
Cite
@article{arxiv.1906.05463,
title = {Combinatorially equivalent hyperplane arrangements},
author = {Elisa Palezzato and Michele Torielli},
journal= {arXiv preprint arXiv:1906.05463},
year = {2021}
}
Comments
Accepted to Advances of Applied Mathematics