English

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 σ\sigma-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