Projective dimension of weakly chordal graphic arrangements

verfasst von

Takuro Abe, Lukas Kühne, Paul Mücksch, Leonie Mühlherr

Abstract

A graphic arrangement is a subarrangement of the braid arrangement whose set of hyperplanes is determined by an undirected graph. A classical result due to Stanley, Edelman and Reiner states that a graphic arrangement is free if and only if the corresponding graph is chordal, i.e., the graph has no chordless cycle with four or more vertices. In this article we extend this result by proving that the module of logarithmic derivations of a graphic arrangement has projective dimension at most one if and only if the corresponding graph is weakly chordal, i.e., the graph and its complement have no chordless cycle with five or more vertices.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Externe Organisation(en)

Rikkyo University
Universität Bielefeld

Typ

Artikel

Journal

Seminaire Lotharingien de Combinatoire

Band

8

Publikationsdatum

03.03.2025

Publikationsstatus

Elektronisch veröffentlicht (E-Pub)

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Diskrete Mathematik und Kombinatorik

Elektronische Version(en)

https://doi.org/10.5802/alco.403 (Zugang: Offen)
https://doi.org/10.48550/arXiv.2307.06021 (Zugang: Offen)