On the geometry of the O'Grady six dimensional irreducible holomorphic symplectic manifold.
Antonio Rapagnetta (Roma Tor Vergata)
Sala Riunioni al piano C - Wednesday, March 8, 2017 h.15:00
Abstract. Few examples of irreducible holomorphic symplectic manifolds are known.
For every even number $2n>2$, two deformation equivalence classes of dimension 2n were exhibited by Beauville in 1983: the Hilbert scheme of n points on a K3 surface and the Kummer generalized variety of dimension 2n of an abelian surface.
About 20 years ago O'Grady discovered two more examples in dimension 6 and 10.
Apart from these, no other example is known up to deformation.
In this talk I will recall the definition of the O'Grady 6 dimensional example and I will give a new way to construct it that allows to compute its Hodge numbers.
This is a joint work with G. Mongardi and G. Sacca'.
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