My research interests concern mainly the theory of Irreducible Symplectic Varieties, both smooth and singular, with particular attention to those that arise from moduli spaces of sheaves on K3 and Abelian surfaces. At the moment, I'm focused on problems regarding the bimeromorphic classification of such varieties, related to and motivated by Torelli Theorem for irreducible symplectic varieties.
The subject of my PhD Thesis is the description of the locally trivial monodromy group of singular moduli spaces of sheaves on Abelian surfaces.
Further topics I'm currently interested in include:
Birationality of moduli spaces of sheaves on Abelian surfaces and relation with wall-crossing for Bridgeland Stability conditions.
Moduli spaces of stable atomic objects on hyperkähler manifolds and their cohomology.
Fano fourfolds of K3 type and link with hyperkähler geometry.
Preprints
Locally trivial monodromy of moduli spaces of sheaves on Abelian surfaces, Ludovica Buelli. ArXiv preprint 2025 (arXiv:2510.23193v2).
Abstract: The aim of this work is to give a description of the locally trivial monodromy group of irreducible symplectic varieties arising from moduli spaces of semistable sheaves on Abelian surfaces with non-primitive Mukai vector. The outcome is that the locally trivial monodromy group of a singular moduli space of this type is isomorphic to the monodromy group of a smooth moduli space, extending Markman’s and Mongardi's description to the non-primitive case. As a consequence, we also prove the SYZ conjecture for any singular moduli space of this type.