Rational Curves and Holomorphic Symplectic Manifolds

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
127 Conference Room, Building No.3
Manfred Lehn
Universität Mainz

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.

Poster (PDF)