Regularity of line configurations

Bruno Benedetti, Michela Di Marca, Matteo Varbaro

Research output: Contribution to journalArticle

2 Citations (Scopus)

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)
JournalJournal of Pure and Applied Algebra
DOIs
StateAccepted/In press - Jan 1 2017

Fingerprint

Regularity
Configuration
Line
Arrangement
Castelnuovo-Mumford Regularity
Graded Algebra
Simplicial Complex
Gorenstein
Nerve
Intersect
Converse
Homology
Trivial
Singularity
Ring
Standards
Interpretation

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Regularity of line configurations. / Benedetti, Bruno; Di Marca, Michela; Varbaro, Matteo.

In: Journal of Pure and Applied Algebra, 01.01.2017.

Research output: Contribution to journalArticle

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