Regularity of line configurations

Bruno Benedetti, Michela Di Marca, Matteo Varbaro

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We show that in arithmetically-Gorenstein line arrangements with only planar singularities, each line intersects the same number of other lines. This number has an algebraic interpretation: it is the Castelnuovo–Mumford regularity of the coordinate ring of the arrangement. We also prove that every (d−1)-dimensional simplicial complex whose 0-th and 1-st homologies are trivial is the nerve complex of a suitable d-dimensional standard graded algebra of depth ≥3. This provides the converse of a recent result by Katzman, Lyubeznik and Zhang.

Original languageEnglish (US)
Pages (from-to)2596-2608
Number of pages13
JournalJournal of Pure and Applied Algebra
Volume222
Issue number9
DOIs
StatePublished - Sep 2018

ASJC Scopus subject areas

  • Algebra and Number Theory

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