Recent preprints & working papers
🔨
Monodromy conjecture for ...
(Work in progress with E. León-Cardenal, W. Veys, J. Viu-Sos).
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Mixed Hodge Structure and complex Jordan form of Yomdin-Lê Surface Singularities.
(Work in progress).
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Computing the preimage of a left ideal under a G-algebra morphism.
(Work in progress with V. Levandovskyy).
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Delta invariant of curves on rational surfaces II: Poincaré series and topological aspects.
(Work in progress with J.I. Cogolludo, T. László, and A. Némethi).
Preprint at
arXiv:2003.07110.
📬
An algorithm for annihilator and Bernstein-Sato polynomial of a meromorphic function.
(Submitted with M. González-Villa, E. León-Cardenal, V. Levandovskyy).
Preprint at
arXiv:2602.00280.
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Modules of logarithmic derivations in wegihted projective spaces and applications to free divisors.
(Submitted with W. Ng Kwing King).
Preprint at
arXiv.org:2603.26574.
📬
On the poles of zeta functions for finite morphisms between normal surfaces.
(Submitted bwith E. León-Cardenal, W. Veys, and J. Viu-Sos).
Preprint at
arxiv.org:2605.17452.
Main publications
2025 – 2027
[28]
Ordinary r-tuples in cyclic quotient surface singularities
(with J.I. Cogolludo, T. László, and A. Némethi).
Accepted in Contemp. Math. Amer. Math. Soc., 2025.
2022 – 2024
[27]
Duality for Poincaré series of surfaces and delta invariant of curves,
(with J.I. Cogolludo, T. László, and A. Némethi),
Res. Math. Sci. 47 (2024), no. 11, 01–18.
arXiv ZAGUAN
[26]
Counting points with Riemann-Roch formulas,
Rev. Real Academia de Ciencias. Zaragoza. 79 (2024), 35–69.
ZAGUAN
RACZ
[25]
Cyclic coverings of rational normal surfaces which are quotients of a product of curves
(with E. Artal and J.I. Cogolludo),
Publ. Mat. 68 (2024), 359–406.
ZAGUAN
[24]
Normal surface singularities with an integral homology sphere link related to space monomial curves with a plane semigroup
(with L. Vos),
Period. Math. Hung. 86 (2023), 303–335.
[23]
Cyclic branched coverings of surfaces with abelian quotient singularities
(with E. Artal and J.I. Cogolludo),
Indiana Univ. Math. J. 71 (2022), no. 1, 213–249.
[22]
Delta invariant of curves on rational surfaces I. The analytic approach
(with J.I. Cogolludo, T. László, and A. Némethi),
Commun. Contemp. Math. 24 (2022), no. 07, Paper No. 2150052, 23 pp.
2019 – 2021
[21]
Bivariate trinomials over finite fields
(with M. Avendaño),
Houston J. Math. 47 (2021), no. 3, 535–552.
HJM
[20]
The monodromy conjecture for a space monomial curve with a plane semigroup
(with W. Veys and L. Vos),
Publ. Mat. 65 (2021), no. 2, 529–597.
[19]
Triangular curves and cyclotimic Zariski tuples
(with E. Artal and J.I. Cogolludo),
Collect. Math. 71 (2020), 427–450.
[18]
Motivic zeta functions on Q-Gorenstein varieties
(with E. León-Cardenal, W. Veys, and J. Viu-Sos),
Adv. Math. 370 (2020) 107192, 34 pp.
[17]
Note on the monodromy conjecture for a space monomial curve with a plane semigroup
(with H. Mourtada, W. Veys, and L. Vos),
Compt. Rendus Maths. 358 (2020) no. 2, pp. 177–187.
CRMath
[16]
The correction term for the Riemann-Roch formula of quotient singularities and associated invariants
(with J.I. Cogolludo),
Rev. Mat. Complut. 32 (2019), 419–450.
2016 – 2018
[15]
Wirtinger curves, Artin groups, and hypocycloids
(with E. Artal and J.I. Cogolludo),
Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. 112 (2018), no. 3, 641–656.
[14]
An algebraic approach to the minimum-cost multi-impulse orbit transfer problem
(with M. Avendaño, V. Martín, and J. Ortigas),
J. Guid. Control Dynam. 39 (2016), no. 8, 1734–1743.
[13]
Semistable Reduction of a Normal Crossing Q-Divisor,
Ann. Mat. Pur. Appl. 195 (2016), no. 5, 1749–1769.
[12]
Numerical Adjunction Formulas for Weighted Projective Planes and Counting Lattice Points
(with J.I. Cogolludo and and J. Ortigas),
Kyoto J. Math. 56 (2016), no. 3, 575–598.
2013 – 2015
[11]
2-Jordan Blocks for the Eigenvalue λ = 1 of Yomdin-Lê Surface Singularities,
C. R. Acad. Sci. Paris, Ser. I 353 (2015), 161–165.
CRMath
[10]
Cartier and Weil Divisors on Varieties with Quotient Singularities
(with E. Artal and J. Ortigas),
Int. J. Math. 25 (2014), no. 11, 1450100, 20 pp.
[9]
Intersection Theory on Abelian-Quotient V-Surfaces and Q-Resolutions
(with E. Artal and J. Ortigas),
J. Singul. 8 (2014), 11–30.
[8]
Local invariants on quotient singularities and a genus formula for weighted plane curves
(with J.I. Cogolludo and J. Ortigas),
Int. Math. Res. Notices 2014, no. 13, 3559–3581.
[7]
Embedded Q-Resolutions for Yomdin-Lê Surface Singularities,
Isr. J. Math. 204 (2014), no. 1, 97–143.
[6]
Monodromy Zeta Function Formula for Embedded Q-Resolutions,
Rev. Mat. Iberoam. 29 (2013), no. 3, 939–967.
2010 – 2012
[5]
Algorithms for Checking Rational Roots of b-functions and their Applications
(with V. Levandovskyy),
J. Algebra 352 (2012), no. 1, 408–429.
[4]
Graded Betti number of the logarithmic derivation module
(with M.A. Marco-Buzunáriz),
Comm. Algebra 38 (2010), no. 11, 4348–4361.
[3]
On the number of irreducible components of the representation variety of a family of one-relator groups
(with A.M. Oller-Marcén),
Internat. J. Algebra Comput. 20 (2010), no. 1, 77–87.
2007 – 2009
[2]
Combinatorial aspects of the character variety of a family of one-relator groups
(with A.M. Oller-Marcén),
Topology Appl. 156 (2009), no. 14, 2376–2389.
[1]
Gröbner bases and the number of Latin squares related to autotopisms of order ≤ 7
(with R.M. Falcón),
J. of Symbolic Comput. 42 (2007), no. 11-12, 1142–1154.
latinSquare.lib
Proceedings & book chapters in MathSciNet
📚
Local invariants of minimal generic curves on rational surfaces
(with J.I. Cogolludo, T. László, and A. Némethi).
p-Adic Analysis, Arithmetic and Singularities, 231–258,
Contemp. Math., 778,
Amer. Math. Soc., 2022.
📚
Cremona transformations of weighted projective planes, Zariski pairs, and rational cuspidal curves
(with E. Artal and J.I. Cogolludo).
Singularities and their interaction with geometry and low dimensional topology—in honor of András Némethi, 117–157,
Trends Math.,
Birkhäuser/Springer, Cham, 2021.
ZAGUAN
📚
Coverings of rational ruled normal surfaces
(with E. Artal and J.I. Cogolludo).
Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics.
Festschrift for Antonio Campillo on the Occasion of his 65th Birthday.
Springer, 343–373, 2018.
ZAGUAN
📚
Q-Resolutions and Intersection Numbers
(with E. Artal and J. Ortigas-Galindo).
Eleventh International Conference Zaragoza-Pau on Applied Mathematics and Statistics, 13–23,
Monogr. Mat. García Galdeano, 37,
Prensas Univ. Zaragoza, Zaragoza, 2012.
PUZ
Zgz-Pau-2012.pdf
📚
Principal intersection and Bernstein-Sato polynomial of an affine variety
(with D. Andres and V. Levandovskyy).
ISSAC 2009—Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, 231–238,
ACM, New York, 2009.
Winner of the 2009 ISSAC
Distinguished Paper Award.
ZAGUAN
todo.pdf
📚
Computational D-module theory with SINGULAR, comparison with other systems and two new algorithms.
(with V. Levandovskyy).
ISSAC 2008, 173–180,
ACM,
New York, 2008.
ZAGUAN
todo.pdf
Other refereed informative articles for general audience
📜
Computing Volumes of Solids of Revolution with Double Integrals
(with A.M. Oller-Marcén).
College Math. J. 45 (2014), no. 3, 219–221.
📜
Constructive D-module theory with Singular.
(with D. Andres, M. Brickenstein, V. Levandovskyy, and H. Schönemann).
Math. Comput. Sci. 4 (2010), no. 2-3, 359–383.
📰
Empleo didáctico de juegos que se matematizan mediante grafos. Una experiencia
(with J.M. Muñoz and A.M. Oller).
Contextos Educativos: Revista de Educación 12 (2009), 137–164.
Dialnet
📰
Sudokus and Gröbner bases: not only a divertimento
(with J. Gago, I. Hartillo, and J.M. Ucha).
Computer algebra in scientific computing, 155–165, Lecture Notes in Comput. Sci., 4194,
Springer,
Berlin, 2006.
US
sudoku.lib
Software (SageMath and Singular)
💿
APLK.ipynb
(with Alquézar-Baeta and M.A. Marco-Buzunáriz).
A
SageMath
library for computing the minimal model of an APL of a simplicial complex.
(
Work in progress)
💿
stratbfun.lib
(with D. Andres and V. Levandovskyy).
A Singular 3.0 library for computing the stratification associated with local b-functions (2011).
It will be available at
SINGULAR.
💾
dmodideal.lib
(with D. Andres and V. Levandovskyy).
A Singular 3.0 library for computations with algebraic D-modules for varieties (2010).
Available at
SINGULAR.
💾
dmodvar.lib
(with D. Andres and V. Levandovskyy).
A Singular 3.0 library for computations with algebraic D-modules for varieties (2008).
Available at
SINGULAR.
💾
dmod.lib
(with V. Levandovskyy).
A Singular 3.0 library for computations with algebraic D-modules (2005).
Available at
SINGULAR.
