Algebraic properties of Levi graphs associated with curve arrangements

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 consider the projective dimension and the Castelnuovo-Mumford regularity for these edge ideals. We provide effective lower and upper bounds on them. As a by-product of our study, we connect, in general, various Buchsbaum properties of squarefree modules.