Publicaciones

We prove effective versions of algebraic and analytic Lang’s conjectures for product-quotient surfaces of general type with $P_g=0$ and $c^2_1=c_2$.
Annali della Scuola Normale di Pisa, 2018

Defensa de tesis

In this thesis, we are interested in the geometry of algebraic varieties that appear as minimal resolutions of quotients of the product of curves by the action of a finite group. We then study the positivity of their cotangent bundle because of its many geometric implications and the valuable and useful information that can be obtained in order to approach some difficult problems such as the famous conjectures of Lang, Lang-Vojta and Green-Griffiths-Lang which in particular give strong constraints on the distribution of the rational curves in varieties of general type. In the case of dimension two, we give a criterion for the positivity of the cotangent bundle and we study the algebraic hyperbolicity of product-quotient surfaces. These results apply to the case of product-quotient surfaces of general type with geometric genus, irregularity and second Segre number equal to zero, for which we prove effective versions of the conjectures mentioned above. More generally in higher dimension, we obtain a criterion for the positivity of the cotangent bundle in the case of smooth quotients and we study in detail the case of the symmetric products of curves.

Posters y Conferencias

In this talk, we are interested in a particular case of Shimura varieties, namely, in quotients of products of curves of genus $\geq 2$ …

In this introductory talk, we give definitions and provide examples motivating the study of the geometry of entire curves.

We prove effective versions of algebraic and analytic Lang’s conjectures for product-quotient surfaces of general type with …

We prove effective versions of algebraic and analytic Lang’s conjectures for product-quotient surfaces of general type with …

We prove effective versions of algebraic and analytic Lang’s conjectures for product-quotient surfaces of general type with …

Nous démontrons des versions algébrique et analytique de la conjecture de Lang pour des surfaces produit-quotient de type général avec …

Nous démontrons des versions algébrique et analytique de la conjecture de Lang pour des surfaces produit-quotient de type général avec …