  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.
