We give a purely combinatorial characterization of complete Stanley–Reisner rings having a principally generated (equivalently, finitely generated) Cartier algebra.

For a polynomial ring R = k[x1, ..., xn], we present an algorithm for computing the characteristic cycle of the localization Rf for any nonzero polynomial f ∈ R. The approach is useful to answer certain questions regarding ...

We give a new algorithm that computes the jumping numbers with their multiplicities and multiplier ideals of any ideal in a regular two-dimensional local ring.

We study the structure of D -modules over a ring R which is a direct sum- mand of a polynomial or a power series ring S with coefficients over a field. We relate properties of D -modules over R to D -modules over S . We ...

We study the generation of the Frobenius algebra of the injective hull of a complete Stanley-Reisner ring over a field with positive characteristic. In particular, by extending the ideas used by M. Katzman to give a ...

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 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 ...

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 ...