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Classical Algebraic Geometry Today |
| January 26, 2009 to January 30, 2009 |
| Organized By: Lucia Caporaso (U. Rome III), Brendan Hassett (Rice U.), James McKernan (MIT), Mircea Mustata (U. Michigan), Mihnea Popa (U. Illinois - Chicago) |
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| Parent Programs: |
| Algebraic Geometry |
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| Return to Workshop Description |
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Four-dimensional analogues of K3 surfaces.
Friday January 30, 2009
11:00AM - 12:00PM
Speakers:
Kieran O'Grady
Abstract:
A compact irreducible hyperk¨ahler (HK) manifold is a simply connected compact K¨ahler manifold carrying a holomorphic symplectic form spanning H2,0. A HK surface is the same as a K3 surface. Among higher – dimensional examples of HK manifolds there are Hilbert schemes parametrizing length-n zero- dimensional subschemes of a K3 and their deformations. We will present a program which aims to prove that if a HK4-fold has cohomology ring isomorphic to that of Hilb2(K3) then it is a deformation of Hilb2(K3) and moreover that a birational Global Torelli holds for this class of manifolds. In particular we will discuss one step in the program: Global Torelli for doube covers of EPW- sextics.
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