Combinatorially equivalent hyperplane arrangements

Elisa Palezzato; Michele Torielli

doi:10.1016/j.aam.2021.102202

Combinatorially equivalent hyperplane arrangements

Elisa Palezzato, Michele Torielli

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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-Gröbner bases. Moreover, we prove that the Terao's conjecture over finite fields implies the conjecture over the rationals.

Original language	English (US)
Article number	102202
Journal	Advances in Applied Mathematics
Volume	128
DOIs	https://doi.org/10.1016/j.aam.2021.102202
State	Published - Jul 2021
Externally published	Yes

Keywords

Combinatorially equivalent
Hyperplane arrangements
Lattice of intersections
Modular methods
Terao's conjecture

ASJC Scopus subject areas

Applied Mathematics

Access to Document

10.1016/j.aam.2021.102202

Cite this

@article{4a78c5b52f22433da8c1b48d106b799b,

title = "Combinatorially equivalent hyperplane arrangements",

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-Gr{\"o}bner bases. Moreover, we prove that the Terao's conjecture over finite fields implies the conjecture over the rationals.",

keywords = "Combinatorially equivalent, Hyperplane arrangements, Lattice of intersections, Modular methods, Terao's conjecture",

author = "Elisa Palezzato and Michele Torielli",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

year = "2021",

month = jul,

doi = "10.1016/j.aam.2021.102202",

language = "English (US)",

volume = "128",

journal = "Advances in Applied Mathematics",

issn = "0196-8858",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Combinatorially equivalent hyperplane arrangements

AU - Palezzato, Elisa

AU - Torielli, Michele

PY - 2021/7

Y1 - 2021/7

N2 - 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-Gröbner bases. Moreover, we prove that the Terao's conjecture over finite fields implies the conjecture over the rationals.

AB - 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-Gröbner bases. Moreover, we prove that the Terao's conjecture over finite fields implies the conjecture over the rationals.

KW - Combinatorially equivalent

KW - Hyperplane arrangements

KW - Lattice of intersections

KW - Modular methods

KW - Terao's conjecture

UR - https://www.scopus.com/pages/publications/85104976091

UR - https://www.scopus.com/inward/citedby.url?scp=85104976091&partnerID=8YFLogxK

U2 - 10.1016/j.aam.2021.102202

DO - 10.1016/j.aam.2021.102202

M3 - Article

AN - SCOPUS:85104976091

SN - 0196-8858

VL - 128

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

M1 - 102202

ER -

Combinatorially equivalent hyperplane arrangements

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this