Luis Núñez-Betancourt







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Duranguenses

USA




Me especializo en Álgebra Conmutativa y sus aplicaciones a la Geometría Algebraica. Particularmente estoy interesado en la cohomología local, los números de Lyubeznik, y la teoría de D-módulos en todas las características (cero, prima y mixta). También trabajo en métodos en característica positiva; en particular, en la teoria deF-modulos, los F-umbrales, clausura hermética (tight closure), y los ideales de la prueba (test ideals). También estoy interesado en invariantes homológicos, como la dimensión proyectiva y la regularidad Castelnuovo-Mumford. Recientemente he estado interesado en ideales binomiales asociados a grafos y a potencias simbólicas de ideales. Antes de mudarme a CIMAT, mi investigación fue parcialmente financiada por el proyecto NSF DMS 1502282.








Lista de artículos:



1.
"Ideals with Larger Projective Dimension and Regularity" (con Jesse Beder, Jason McCullough, Alexandra Seceleanu, Bart Snapp and Branden Stone), Journal of Symbolic Computation, Vol. 46, Num. 10, Octubre 2011, Pag. 1105-1113.



arxiv
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2.
"Local cohomology properties of direct summands", Journal of Pure Applied and  Algebra 216 (2012) No. 10, Pag. 2137-2140.



arxiv
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3.
"On certain rings of differentiable type and finiteness properties of local cohomology", Journal of Algebra, Vol. 379, Abril 2013, Pages 1-10.



arxiv
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4.
Local cohomology modules of polynomial or power series rings over rings of small dimension", Illinois Journal of Mathematics, Volume 57, No. 1 (2013), Pag. 279-294.



arxiv journal









5.
"Lyubeznik numbers in mixed characteristic" (con Emily E. Witt), Mathematical Research Letters, Volume 20, No. 6 (2013), Pag. 1125-1143.



arxiv journal









6.
"Associated primes of local cohomology of flat extensions with regular fibers and Σ-finite D-modules", Journal of Algebra, Vol. 399, Feb. 2014, Pag. 770-781.



arxiv journal









7.
"Generalized Lyubeznik numbers" (with Emily E. Witt), Nagoya Journal of Mathematics, Vol. 215 (2014), Pag. 168-202.



arxiv journal









8.
"Properties of Lyubeznik numbers under localization and polarization'' (with Arindam Banerjee and Kohji Yanagawa), Journal of Pure and Applied Algebra 219 (2015), No. 11, Pag. 4872-4888.



arxiv journal









9.
"F-jumping and F-Jacobian ideals for hypersurfaces" (with Felipe Pérez), Journal Pure and Applied Algebra, Vol. 220, Num. 1, Enero 2016, Pag. 292-318.



arxiv journal









10.
"A sufficient condition for strong F-regularity'' (with Alessandro De Stefani),  Proceedings of the American Mathematical Society, Vol. 144, Num. 1, Enero 2016, Pag. 21-29.



arxiv journal









11.
A survey on the Lyubeznik numbers" (with Emily E. Witt and Wenliang Zhang), Contemporary Mathematics, Vol. 657 (2016), Pag. 154-181.



arxiv journal









12.
"F-pure thresholds of quasi-homogeneous polynomials" (with Daniel J. Hernández, Emily E. Witt, and Wenliang Zhang), Michigan Mathematical Journal 65 (2016), no. 1, 57-87.



arxiv journal









13.
"Frobenius Betti numbers and modules of finite projective dimension'' (with Alessandro De Stefani, and  Craig Huneke), aceptado in Journal of Commutative Algebra.



arxiv journal









14.
"On the hyperhomology of the small gobelin for codimension 2" (with Xavier Gómez-Mont), aceptado in the Boletín de la Sociedad Matemática Mexicana.



arxiv
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15.
"Binomial edge ideal and graph connectivity" (with Arindam Banerjee), Proceedings of the American Mathematical Society, 145 (2017), no. 2, 487–499.


arxiv journal









16.
"Local m-adic constancy of F-pure thresholds and test ideals for hypersurfaces with isolated singularities", (with Daniel J. Hernández, and Emily E. Witt), aceptado en Mathematical Proceedings of the Cambridge Philosophical Society.








17.
"On the support of local cohomology via Frobenius" (with Mel Hochster),  aceptado en Mathematical Research Letters.








18.
"F-thresholds of graded rings'' (with Alessandro De Stefani), aceptado en Nagoya Mathematical Journal.



arxiv journal









19.
"On the existence of F-thresholds and related limits" (with Alessandro De Stefani and Felipe Pérez), aceptado en Transactions of the American Mathematical Society.



arxiv










20.
"D-modules, Bernstein-Sato polynomials, and F-invariants of direct summands" (with Josep Àlvarez-Montaner and Craig Huneke), accepted pending revisions in Advances in Mathematics.

    arxiv      







21.
Lyubeznik numbers and injective dimension of local cohomology modules''
(with Daniel J. Hernández, Felipe Pérez, and Emily E. Witt), aceptado en Transactions of the American Mathematical Society.









22.
"Cohomological dimension, Lyubeznik numbers, and connectivity in mixed characteristic" (con Daniel J. Hernández, Felipe Pérez, and Emily E. Witt), sometido.
    arxiv      







23.
Symbolic powers of ideals" (con Hailong Dao, Alessandro De Stefani, Craig Huneke, and Eloisa Pires), sometido.









24.
"Hilbert-Kunz Multiplicities and F-thresholds" (con Ilya Smirnov), en preparación