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

Currently I am visiting for ten weeks Professor Prof. Dr. Michael Joswig and Bernd Sturmfels at Institut für Mathematik der Technischen Universität Berlin in the group Fachgebiet Diskrete Mathematik/Geometrie.

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 generelised Kleiman's construction of iterated blow ups to paramertise clusters of sections, which leads 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 flattening stratifications, universal sections families and, of course, blow ups.

**Publications**

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

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

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**Preprints**

(with Sascha Timme & Madeleine Weinstein)

96120: The degree of the linear orbit of a cubic surface

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

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The blow up split section family

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