|Speaker:||Genki Oouchi (Kavli IPMU)|
|Title:||Lagrangian embedding of cubic 4-folds containing a plane|
|Date (JST):||Mon, Mar 03, 2014, 14:00 - 17:00|
|Place:||Seminar Room A|
Lehn et al proved that a cubic fourfold X not containing a plane is embedded into a 8-dimensional holomorphic symplectic variety which is a contraction of the compactified moduli space of twisted cubics on X as a Lagrangian submanifold. I construct a similar Lagrangian embedding of a cubic fourfold containing a plane in a different way. Rationality problem of cubic fourfolds has relation to K3 surfaces at the level of derived categories, Hodge theory. A. Kuznetsov proved that the non-trivial component of the derived category of a cubic fourfold containing a plane is equivalent to the derived category of a twisted K3 surface.
In my construction, 8-dimensional holomorphic symplectic variety is given by a moduli space of stable objects in the derived category of a twisted K3 surface.
In the first part of the talk, I will explain how rationality problem of cubic fourfolds is related to K3 surfaces and describe the main result.
In the second part of the talk, I will explain how to prove the main result.
|Remarks:||Part 1; 14:00 - 15:00
Part 2; 15:30 - 17:00