Algebraic properties of Levi graphs associated with curve arrangements
Piotr Pokora, Tim R\"omer
TL;DR
This paper investigates algebraic properties of edge ideals derived from Levi graphs of plane curve arrangements, providing characterizations and bounds for Cohen-Macaulayness, Buchsbaum properties, and regularity.
Contribution
It introduces combinatorial criteria for algebraic properties of edge ideals from Levi graphs and establishes bounds on projective dimension and regularity.
Findings
Characterization of Cohen-Macaulay, Buchsbaum, and sequentially Cohen-Macaulay properties.
Effective bounds on projective dimension and Castelnuovo-Mumford regularity.
Connection between Buchsbaum properties of squarefree modules.
Abstract
In the present paper we study algebraic properties of edge ideals associated with plane curve arrangements via their Levi graphs. Using combinatorial properties of such Levi graphs we are able to describe those monomial algebras being Cohen-Macaulay, Buchsbaum, and sequentially Cohen-Macaulay. We also condsider the projective dimension and the Castelnuovo-Mumford regularity for these edge ideals. We provide effective lower and upper bounds on them. As a byproduct of our study we connect, in general, various Buchsbaum properties of squarefree modules.
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