In this lecture series, I will try to explain how to use moduli of rational curves to construct holomorphic symplectic (or hyperkähler) manifolds. We will start with a brief introduction to symplectic manifolds and a survey of existing construction methods. We will then have a closer look into Grassmannians, Quot schemes and Hilbert schemes and their use in constructing examples. In particular, I will discuss in some detail the theorems of Beauville and Donagi and of my joint work with N.Addington, C.Lehn, Sorger and van Straten, Depending on the interest of the audience I would also like to discuss the interpretation of some results from the perspective of matrix factorisations and of Kuznetsov's semiorthogonal decomposition of the derived category of cubic fourfolds.
Rational Curves and Holomorphic Symplectic Manifolds
Date
2015/05/13 Wed 14:45 - 16:15
2015/05/27 Wed 14:45 - 16:15
2015/06/03 Wed 14:45 - 16:15
2015/06/10 Wed 14:45 - 16:15
2015/06/17 Wed 14:45 - 16:15
2015/07/01 Wed 14:45 - 16:15
2015/07/08 Wed 14:45 - 16:15
Room
3号館127大会議室
Speaker
Manfred Lehn
Affiliation
Universität Mainz
Abstract