English

Algebraic properties of Levi graphs associated with curve arrangements

Commutative Algebra 2022-08-16 v4 Algebraic Geometry Combinatorics

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.

Keywords

Cite

@article{arxiv.2201.11788,
  title  = {Algebraic properties of Levi graphs associated with curve arrangements},
  author = {Piotr Pokora and Tim Römer},
  journal= {arXiv preprint arXiv:2201.11788},
  year   = {2022}
}

Comments

20 pages. This is the final version incorporating the referee's remarks, to appear in Research in the Mathematical Sciences