Let R = k[x1, . . . , xd] or R = k[[x1, . . . , xd]] be either a polynomial or a formal power series ring in a finite number of variables over a field k of characteristic p > 0 and let DR|k be the ring of klinear differential ...

We provide a Hochster type formula for the local cohomology modules of binomial edge ideals. As a consequence we obtain a simple criterion for the Cohen-Macaulayness of these ideals and we describe their Castelnuovo-Mumford ...

We describe an algorithm deciding if the annihilating ideal of the meromorphic function 1 f , where f = 0 defines an arrangement of hyperplanes, is generated by linear differential operators of order 1. The algorithm is ...

We report recent work on the study of Lyubeznik numbers and their relation to invariants coming from the study of linear strands of free resolutions.

In this work, we introduce a new set of invariants associated to the linear strands of a minimal free resolution of a -graded ideal . We also prove that these invariants satisfy some properties analogous to those of Lyubeznik ...

We prove that sequentially Cohen-Macaulay rings in positive characteristic, as well as sequentially Cohen-Macaulay Stanley-Reisner rings in any characteristic, have trivial Lyubeznik table. Some other configurations of ...

We provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements ...