Research

My research interests are in Algebraic Geometry, in particular I am interested in the study of locally free sheaves (vector bundles) over projective varieties. The study of locally free sheaves supported on a projective variety is a powerful tool to understand its geometry.

I deal with particular classes of sheaves, namely arithmetically Cohen-Macaulay (aCM), Ulrich and Instanton sheaves supported on varieties of low dimension. The study of such sheaves supported on a variety gives us a measure of the complexity of the variety itself. For example the projective space of any dimension is characterized by Horrock’s theorem by the property that a vector bundle is aCM if and only if it is totally decomposable. Moreover I am interested in the study of the parameter spaces (moduli spaces) of these objects, investigating properties like smoothness, irreducibility and rationality. In this context, I use tools from Derived Categories of sheaves which allow to express a coherent sheaf as the degeneracy object of a spectral sequence (or a resolution in particular cases).

In my current research projects I am dealing with the existence of Ulrich and instanton sheaves over projective hypersurfaces of arbitrary degree and dimension, and with the description of the moduli spaces of instanton sheaves on Fano 3-folds.