Now showing items 1-20 of 55

• #### A Koszul complex over skew polynomial rings ﻿

(2019-01-01)
Article
Open Access
We construct a Koszul complex in the category of left skew polynomial rings associated with a flat endomorphism that provides a finite free resolution of an ideal generated by a Koszul regular sequence
• #### A surprising fact about D-modules in characteristic p>0 ﻿

(2004)
Research report
Open Access
Let R = k[x1, . . . , xd] be the polynomial ring in d independent variables, where k is a field of characteristic p > 0. Let DR be the ring of k-linear differential operators of R and let f be a polynomial in R. In this ...
• #### Addendum to "Frobenius and Cartier algebras of Stanley-Reisner rings" [J.Algebra 358 (2012), 162-177] ﻿

(2013-05)
Research report
Open Access
We give a purely combinatorial characterization of complete Stanley-Reisner rings having a principally generated (equivalently, nitely generated) Cartier algebra
• #### Addendum to “Frobenius and Cartier algebras of Stanley–Reisner rings” [J. Algebra 358 (2012) 162–177] ﻿

(2014-09)
Article
Restricted access - publisher's policy
We give a purely combinatorial characterization of complete Stanley–Reisner rings having a principally generated (equivalently, finitely generated) Cartier algebra.
• #### Bass numbers of local cohomology of cover ideals of graphs ﻿

(2020)
Article
Open Access
We develop splitting techniques to study the 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 ...
• #### Bass numbers of local cohomology of cover ideals of graphs ﻿

(2019)
Research report
Open Access
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 ...
• #### Bernstein's inequality and holonomicity for certain singular rings ﻿

(2021)
Research report
Open Access
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 ...
• #### Bernstein-Sato functional equations, v -filtrations, and multiplier ideals of direct summands ﻿

(2021-01-01)
Article
Open Access
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 ...
• #### Bernstein-Sato functional equations, V-filtrations, and multiplier ideals of direct summands ﻿

(2019)
Research report
Open Access
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 ...
• #### Bernstein-Sato polynomials in commutative algebra ﻿

(Springer Nature, 2022-02-23)
Part of book or chapter of book
Restricted access - publisher's policy
This is an expository survey on the theory of Bernstein-Sato polynomials with special emphasis in its recent developments and its importance in commutative algebra
• #### Characteristic cycle of local cohomology modules of monomial ideals II ﻿

(2003)
Article
Open Access
• #### Characteristic cycles of local cohomology modules of monomial ideals ﻿

(1998)
Article
Open Access
By using the theory of D-modules we express the characteristic cycle of a local cohomology module supported on a monomial ideal in terms of conormal bundles relative to a subvariety. As a consequence we can decide when a ...
• #### Characteristic cycles of localizations: algorithmic approach ﻿

(2004)
Article
Open Access
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 ...
• #### Cohomología local con soporte un ideal monomial (D-módulos y combinatoria) ﻿

(2000)
Article
Open Access
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 ...
• #### Cohomología local con soporte un ideal monomial (D-módulos y combinatoria) ﻿

(Edicions UPC, 2000)
Conference report
Restricted access - publisher's policy
We study, by using the theory of algebraic D-modules, the local cohomology modules supported on a monomial ideal I of the polynomial ring R = k[x1, . . . , xn], where k is a field of characteristic zero. We compute the ...
• #### Computing jumping numbers and multiplier ideals in two-dimensional regular local rings ﻿

(Universitat de Barcelona. Edicions i Publicacions, 2014)
Conference report
Restricted access - publisher's policy
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.
• #### Constancy regions of mixed multiplier ideals in two-dimensional local rings with rational singularities ﻿

(WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2018)
Article
Open Access
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 ...
• #### D-modules, Bernstein-Sato polynomials and F-invariants of direct summands ﻿

(2017-12-01)
Article
Open Access
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 ...
• #### Divisors of expected Jacobian type ﻿

(2020)
Research report
Open Access
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 ...
• #### Divisors of expected Jacobian type ﻿

(2021)
Article
Open Access
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 ...