## Laura Brustenga i Moncusí

Department of Mathematical Sciences
Københavns Universitet
Universitetsparken 5
DK-2100 Copenhagen Ø

email: brust AT math.ku.dk

I am a PostDoc as part of the group Mathematics of reaction networks, under the supervisoin of Elisenda Feliu at Department of Mathematical Sciences of KU
My research interests are in pure and aplied Algebraic Geometry. On the pure side, 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. On the aplied side, I started working on Numerical Algebraci Geometry and Chemical Reaction Networks.

### PhD project: Parametrising clusters of sections

We study the parameter space for clusters of sections of a family. We 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.
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### 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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(with Sascha Timme & Madeleine Weinstein)
96120: The degree of the linear orbit of a cubic surface
to appear in Le Matematiche.
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### Preprints

(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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