## Laura Brustenga i Moncusí

Departament de Matemàtiques
Facultat de Ciències, C1/310
Universitat Autònoma de Barcelona
08193 Bellaterra (Barcelona)

email: brust AT mat.uab.cat
Tel: (+34) 93 581 35 65
Fax: (+34) 93 581 27 90

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