Laura Brustenga i Moncusí

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

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

Brustenga i Moncusí, L. picture

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.


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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(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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