9 citations · 27 across the 16 of their papers we have counts for
32 papers
Bernstein-Sato theory for singular rings in positive characteristic
Jack Jeffries, Luis Núñez-Betancourt, Eamon Quinlan-Gallego
The Bernstein-Sato polynomial is an important invariant of an element or an ideal in a polynomial ring or power series ring of characteristic zero, with interesting connections to…
Blowup algebras of determinantal ideals in prime characteristic
Alessandro De Stefani, Jonathan Montaño, Luis Núñez-Betancourt
We study when blowup algebras are -split or strongly -regular. Our main focus is on algebras given by symbolic and ordinary powers of ideals of minors of a generic matrix, a…
Bernstein-Sato polynomials in commutative algebra
Josep Àlvarez Montaner, Jack Jeffries, Luis Núñez-Betancourt
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.
Bernstein's inequality and holonomicity for certain singular rings
Josep Àlvarez Montaner, Daniel J. Hernández, Jack Jeffries +3
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…
Poincaré series of multiplier and test ideals
Josep Àlvarez Montaner, Luis Núñez-Betancourt
We prove the rationality of the Poincaré series of multiplier ideals in any dimension and thus extending the main results for surfaces of Galindo and Monserrat and Alberich-Carrami…
Bounds for the Minimum Distance Function
Luis Núñez-Betancourt, Yuriko Pitones, Rafael H. Villarreal
Let be a homogeneous ideal in a polynomial ring . In this paper, we extend the study of the asymptotic behavior of the minimum distance function of and give bounds…
-thresholds and test ideals of Thom-Sebastiani type polynomials
Manuel González Villa, Delio Jaramillo-Velez, Luis Núñez-Betancourt
We provide a formula for -thresholds of a Thom-Sebastiani type polynomial over a perfect field of prime characteristic. This result extends the formula for the -pure threshol…
Connectedness of square-free Groebner Deformations
Lilia Alanís-López, Luis Núñez-Betancourt, Pedro Ramírez-Moreno
Let be a homogeneous ideal equipped with a monomial order . We show that if is a square-free monomial ideal, then …
Symbolic powers of determinantal ideals in prime characteristic
Jonathan Montaño, Luis Núñez-Betancourt
We study the symbolic powers of determinantal ideals of generic, generic symmetric, and Hankel matrices of variables, and of Pfaffians of generic skew-symmetric matrices, in prime…
Higher Nash blowups of normal toric varieties in prime characteristic
Daniel Duarte, Luis Núñez-Betancourt
We prove that the higher Nash blowup of a normal toric variety defined over a field of positive characteristic is an isomorphism if and only if it is non-singular. We also extend a…
Nash blowups in prime characteristic
Daniel Duarte, Luis Núñez-Betancourt
We initiate the study of Nash blowups in prime characteristic. First, we show that a normal variety is non-singular if and only if its Nash blowup is an isomorphism, extending a th…
-Volumes
Wágner Badilla-Céspedes, Luis Núñez-Betancourt, Sandra Rodríguez-Villalobos
In this work we define a numerical invariant called -volume. This number extends the definition of -threshold of a pair of ideals and , to a sequence of ideal…
Bernstein-Sato functional equations, -filtrations, and multiplier ideals of direct summands
Josep Àlvarez Montaner, Daniel J. Hernández, Jack Jeffries +3
This paper investigates the existence and properties of a Bernstein-Sato functional equation in nonregular settings. In particular, we construct -modules in which such formal eq…
Quantifying singularities with differential operators
Holger Brenner, Jack Jeffries, Luis Núñez-Betancourt
The -signature of a local ring of prime characteristic is a numerical invariant that detects many interesting properties. For example, this invariant detects (non)singularity an…
Splittings and symbolic powers of square-free monomial Ideals
Jonathan Montaño, Luis Núñez-Betancourt
We study the symbolic powers of square-free monomial ideals via symbolic Rees algebras and methods in prime characteristic. In particular, we prove that the symbolic Rees algebra a…
Footprint and minimum distance functions
Luis Núñez-Betancourt, Yuriko Pitones, Rafael H. Villarreal
Let be a polynomial ring over a field , with a monomial order , and let be an unmixed graded ideal of . In this paper we study two functions associated to :…
Connectedness and Lyubeznik numbers
Luis Núñez-Betancourt, Sandra Spiroff, Emily Witt
We investigate the relationship between connectedness properties of spectra and the Lyubeznik numbers, numerical invariants defined via local cohomology. We prove that for complete…
Local cohomology and Lyubeznik numbers of -pure rings
Alessandro De Stefani, Eloísa Grifo, Luis Núñez-Betancourt
In this article, we study certain local cohomology modules over -pure rings. We give sufficient conditions for the vanishing of some Lyubeznik numbers, derive a formula for comp…
-vectors of chordal graphs
Luis Pedro Montejano, Luis Núñez Betancourt
The -vector of a graph is defined in terms of its clique vector by the equation $\sum^d_{i=1}b_i(x+1)^{i-1}=\sum^d_{i=1} c_i x^{i…
Symbolic powers of ideals
Hailong Dao, Alessandro De Stefani, Eloísa Grifo +2
We survey classical and recent results on symbolic powers of ideals. We focus on properties and problems of symbolic powers over regular rings, on the comparison of symbolic and re…
-modules, Bernstein-Sato polynomials and -invariants of direct summands
Josep Àlvarez Montaner, Craig Huneke, Luis Núñez-Betancourt
We study the structure of -modules over a ring which is a direct summand of a polynomial or a power series ring with coefficients over a field. We relate properties of $…
On the existence of -thresholds and related limits
Alessandro De Stefani, Luis Núñez-Betancourt, Felipe Pérez
The -thresholds are important numerical invariants in prime characteristic, whose existence had been established only under certain assumptions. We show the existence of -thr…
Graph Connectivity and Binomial Edge Ideals
Arindam Banerjee, Luis Núñez-Betancourt
We relate homological properties of a binomial edge ideal to invariants that measure the connectivity of a simple graph . Specifically, we show if $R/\mathcal{J}…
Lyubeznik numbers and injective dimension in mixed characteristic
Daniel J. Hernández, Luis Núñez-Betancourt, Felipe Pérez +1
We investigate the Lyubeznik numbers, and the injective dimension of local cohomology modules, of finitely generated -algebras. We prove that the mixed characteristic L…