Research interests:

Algebraic Geometry, Singularity Theory, Commutative Algebra, Algebraic Foliations, Coding Theory

Publications:

(With C. Galindo) The cone of curves associated to a plane configuration, Commentarii Mathematici Helvetici 80 (2005), 75-93

(With C. Galindo) On the cone of curves and of line bundles of a rational surface, International Journal of Mathematics 15 no. 4 (2004), 393-407

(With C. Galindo) The total coordinate ring of a smooth projective surface, Journal of Algebra 284 no. 1 (2005), 91-101

(With C. Galindo) Algebraic integrability of foliations of the plane, Journal of Differential Equations, 231 no. 2 (2006), 611-632.

Curves having one place at infinity and linear systems on rational surfaces, Journal of Pure and Applied Algebra 211 no. 3 (2007), 685-701

(With C. Galindo) On the characterization of algebraically integrable plane foliations, Transactions of the American Mathematical Society 362, No. 9 (2010) 4557-4568.

(With C. Galindo) Delta-sequences and evaluation codes defined by plane valuations at infinity, Proceedings of the London Mathematical Society 98 no.3 (2009), 714-740.

(With A. Campillo and G. González-Sprinberg) Configurations of infinitely near points, Sao Paulo Journal of Mathematical Sciences 3 no. 1 (2009), 115-160.

(With C. Galindo) The Poincaré series of multiplier ideals of a simple complete ideal in a local ring of a smooth surface, Advances in Mathematics 225 (2010), no. 2, 1046-1068.

Lins-Neto's examples of foliations and the Mori cone of blow-ups of P^2, Bulletin of the London Mathematical Society 43 (2011), no. 2, 335-346.

Fibers of pencils of curves on smooth surfaces, International Journal of Mathematics 22 (2011), no. 10, 1433-1437.

(With C. Galindo) Finite families of plane valuations: value semigroup, graded algebra and Poincaré series. Contemporary Mathematics 516 189-212 (2012).

(With C. Galindo) The Abhyankar-Moh theorem for plane valuations at infinity, J. Algebra 374 (2013), 181-194.

(With F. Hernando and G. McGuire) On the classification of exceptional planar functions over F_p, Geom. Dedicata 173 (2014), 1–35.

(With C. Galindo) The Poincaré problem, algebraic integrability and dicritical divisors. J. Differential Equations 256 (2014), no. 11, 3614–3633.

(With C. Galindo) Evaluation codes defined by finite families of plane valuations at infinity. Des. Codes Cryptogr. 70 (2014), no. 1-2, 189–213.

(With A. Ferragut and C. Galindo) A class of polynomial planar vector fields with polynomial first integral. Journal of Mathematical Analysis and Applications, 430 (2015), 354-380. 

(With C. Galindo and F. Hernando) The log-canonical threshold of a plane curve. Mathematical Proceedings of the Cambridge Philosophical Society 160.3 (2016), 513-535.

(With C. Galindo) The cone of curves and the Cox ring of rational surfaces given by divisorial valuations. Advances in Mathematics, 290 (2016) 1040-1061