We develop splitting techniques to study Lyubeznik numbers of cover ideals of graphs which allow us to describe them for large families of graphs including forests, cycles, wheels and cactus graphs. More generally we are ...

In this manuscript we prove the Bernstein inequality and develop the theory of holonomic D-modules for rings of invariants of finite groups in characteristic zero, and for strongly F-regular finitely generated graded ...

This paper investigates the existence and properties of a Bernstein– Sato functional equation in nonregular settings. In particular, we construct D-modules in which such formal equations can be studied. The existence of ...

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 study, by using the theory of algebraic $\cD$-modules, the local cohomology modules supported on a monomial ideal $I$ of the polynomial ring $R=k[x_1,\dots,x_n]$, where $k$ is a field of characteristic zero. We compute ...

The aim of this paper is to study mixed multiplier ideals associated with a tuple of ideals in a two-dimensional local ring with a rational singularity. We are interested in the partition of the real positive orthant given ...

Divisors whose Jacobian ideal is of linear type have received a lot of attention recently because of its connections with the theory of D-modules. In this work we are interested on divisors of expected Jacobian type, that ...

© 2018 Elsevier Ltd. We provide an algorithm that allows to describe the minimal log-resolution of an ideal in a smooth complex surface from the minimal log-resolution of its generators. In order to make this algorithm ...

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 ...