I am a PhD candidate under the supervision of Prof. Joaquim Roé and supported by Departament de Matemàtiques de la UAB, PIF.

My research interests are mostly in Algebraic Geometry. In particular, I study the geometry of a locally closed subfunctor of the Hilbert functor aiming to obtain sharper upper bounds on the dimension of linear systems of curves on surfaces.

**PhD project** (Poster)

I study the parameter space for clusters of sections of a family. I adapted Kleiman's construction of iterated blow ups to paramertise clusters of sections. This led us to the notion of Universal scheme of cluster of r sections. We show that, as iterated blow ups, such schemes can be constructed iteratively, but now the iterative step is not as simple as blowing up a regularly embedded diagonal of a suitable product. In order to formalise this iterative step we define and study the blow up split sections family, a generalisation of blow ups, which exhibits properties of the flattening stratification, universal sections family and, of course, the blow up.

**Publications**

On the universal scheme of r-relative clusters of a family

*Communications in Algebra*, ** 45 ** (2017), no.6, pp. 2708--2725

|| Bibtex || DOI || Arxiv ||

**Preprints**

The Straight Blow Up Section Family, Arxiv

(with Shreedevi K. Masuti) On the Waring rank of binary forms: The binomial formula and a dihedral cover of rank two forms, Arxiv