Modular vector bundles on hyperkähler manifolds

Name: Modular vector bundles on hyperkähler manifolds
Start: 2025-10-08
End: 2025-10-08

We exhibit examples of slope-stable and modular vector bundles on a hyperkähler manifold of $K3^{[2]}$-type. These are obtained by performing standard linear algebra constructions on the examples studied by O’Grady of (rigid) modular bundles on the Fano varieties of lines of a general cubic $4$-fold and the Debarre-Voisin hyperkähler. Interestingly enough, these constructions are almost never infinitesimally rigid, and more precisely we show how to get (infinitely many) $20$ and $40$ dimensional families. This is a joint work with Claudio Onorati. Time permitting, I will also present a joint work with Alessandro D’Andrea and Claudio Onorati on a connection between discriminants of vector bundles on smooth and projective varieties and representation theory of $GL(n)$