Seminario di algebra e geometria
ore
11:00
presso Aula Vitali
By the Bogomolov decomposition theorem, irreducible holomorphic
symplectic manifolds play a central role in the classification of
compact Kähler manifolds with numerically trivial canonical bundle. Very
recently, Höring and Peternell completed the proof of the existence of a
singular analogue of the Bogomolov decomposition theorem. In view of
this result, singular irreducible symplectic varieties (following Greb,
Kebekus and Peternell) are singular analogue of irreducible holomorphic
symplectic manifolds. In a joint work with Arvid Perego, still in
progress, we show that all moduli spaces of sheaves on projective K3
surfaces are singular irreducible symplectic varieties. We compute their
Beauville form and the Hodge decomposition of their second integral
cohomology, generalizing previous results, in the smooth case, due to
Mukai, O'Grady and Yoshioka.