부산대학교 도서관

In this article, we study algebraic properties of binomial edge ideals of Levi graphs associated with certain plane curve arrangements. Using combinatorial properties of Levi graphs, we discuss the Cohen-Macaulayness of binomial edge ideals of Levi graphs associated to some curve arrangements in the complex projective plane, like the $d$-arrangement of curves and the conic-line arrangements. We also discuss the existence of certain induced cycles in the Levi graphs of these arrangements and obtain lower bounds for the regularity of powers of the corresponding binomial edge ideals.
Comment: Proofs of Theorems 5.1 and 5.5 have been modified, examples 5.6 and 5.7 were added following the suggestion of referee. 19 pages, comments and suggestions are welcome