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Oberseminar WiSe 2011/12 Zusammenfassung des Vortrags von Malte Wandel

Stability of tautological vector bundles on Hilbert schemes of K3 surfaces

Most examples of irreducible holomorphic symplectic manifolds (IHS) arise by constructions related to moduli spaces of sheaves on K3 surfaces. Not much is known about moduli spaces of sheaves on higher dimensional IHS such as Hilbert schemes of points on K3 surfaces. A big class of examples of sheaves on Hilbert schemes are the so-called tautological vector bundles. I will report on recent results on the stability of tautological vector bundles on the Hilbert square of projective K3 surfaces and describe a method to prove smoothness of the corresponding moduli spaces.