Minha área de pesquisa trata de questões enumerativas em Geometria Algébrica.
Tenho também me interessado por singularidades e espaços de folheações holomorfas.

Artigos +- recentes:
·  (com Daniel Leite) Degrees of spaces of foliations of codimension one in CPn. Journal of Pure and Applied Algebra
Resumo: We consider the Zariski closure of the set of foliations in CPn defined by a differential 1-form of type aFdG-bGdF, where F,G denote co-prime homogeneous polynomials of degrees a, b. Gomez-Mont and Lins-Neto have shown that this is an irreducible component of the space of foliations of codimension 1. Our main result gives a closed formula for the degree of this component for a=2, b odd.

Foliations singular along a curve. Transactions of the London Mathematical Society, v. 2, p. 80-92, 2015.
Resumo: A general one-dimensional foliation in the complex projective space has finetely many singularities. Given a family of positive dimensional subschemes in Pn, we study the loci in the space of foliations defined by the requirement that the singularities contain a member of the family. We show that the degrees of the loci are given by a polynomial. We compute it explicitely in a few examples. We also include a formula for the number of isolated singularities of a foliation in Pn general among those which are singular along a smooth curve.

·  (com A. R. Silva), Degree of the variety of pairs of nilpotent commuting matrices. Resumo: We compute the degrees of the projective varieties of pairs of commuting nilpotent matrices of orders n = 2, 3, 4, to wit, 4, 72 and 5440. ( Bulletin of the Brazilian Mathematical Society , vol. dedicado a Steven Kleiman e Aron Simis.) v. 45, p. 837-863, 2014.

·  Hypersurfaces containing unexpected subvarieties.
Resumo: Cubic 4-folds in P5 containing a general pair of 2- planes are known to be rational. They form a family of codimension 2 in P55 . We find a polynomial which encodes, for all d>=3, the degrees of the loci of hypersurfaces in P5 of degree d containing some plane-pair. In particular, we get the degree (3,371,760) of that family of dimension 53 of rational cubic 4folds. (dedicado a Xavier Gomez-Mont) Journal of Singularities, vol. 9, 219-225, 2014.

·  (com Angelo Felice Lopez e Fernando Cukierman) Enumeration of Surfaces Containing an Elliptic Quartic Curve.
Resumo: A very general surface of degree at least four in P3 contains no curves other than intersections with surfaces. We find a formula for the degree of the locus of surfaces in P3 of degree d >= 5 which contain some elliptic quartic curve. We also compute the degree of the locus of quartic surfaces containing an elliptic quartic curve. Beware this is not a special case of the former, due to the fact that if a quartic surface contains an elliptic quartic curve it must contain a pencil of such curves. Proc. Amer. Math. Soc. 142, 3305-3313, 2014.

·  Enumeration of tropes Resumo: Singularities of the plane sections of a general surface in three-space are well known, and counted; in particular, all plane sections are reduced. Fixing integers d, k, we give formulas for the degree of the locus of surfaces of degree d admitting a plane which is tangent along some curve of degree k. Dedicated to Prof. Heisuke Hironaka on his 80th birthday. (RACSAM ), v. 107, p. 213-220, (2013).

·  (com Viviana Ferrer) Degenerate singularities of one dimensional foliations , Comment. Math. Helv. 88, 305-321 (2013)

·  (com José Alberto Duarte Maia, Adriana Rodrigues Silva e Fernando Xavier) Enumeration of surfaces containing a curve of low degree. Resumo: A very general surface of degree at least 4 in P3 contains no curves besides intersection with another surface. Let W be some irreducible subvariety of the Hilbert scheme of curves in P3 . Let NL(W,d) be the set of surfaces of fixed, sufficiently high degree d which contain a member of W . It is a closed subvariety of the linear system of such surfaces. We find polynomial formulas for the degrees of NL(W,d) whenever W consists of curves of the following types: a union of up to three general lines; a conic or a twisted cubic curve. The case of elliptic quartic curves is subtler and treated elsewhere. J. Pure Appl. Algebra 217, no. 8, 1379-1394, (2013)

Livros:
·  (com Joachim Kock)} A fórmula de Kontsevich para curvas racionais planas, 22^o Coloq. Bras.Mat. 1999. PDF

·  Introdução às curvas algébricas planas, Coleção Matemática Universitária, IMPA / SBM, 160 p., 1996.

scripts para o calculo do grau de algumas componentes de espaços de folheações.

·  Scripts em maple para cálculos locais e aplicação da fórmula de Bott para enumeração de cúbicas reversas: zip txt

·  Script para o cálculo do número de curvas canônicas em P3 incidentes 24 retas em posição geral.