Dr. Manfred Lehn

Manfred Lehn (Mainz) visited Laboratory of Algebraic Geometry by the invitation of the research fellow A.Kuznetsov on September 2015

September 24th he read a first part of minicourse "Symplectic manifolds and moduli of rational curves" at the seminar "Geometric structures on complex manifolds"

Abstract: In this lecture series, I will try to explain how to use moduli of rational curves to construct holomorphic symplectic (or hyperkahler) 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.

September 25th he gives a talk "Symplectic hypersurfaces" at the weekly seminar of the Laboratory.

Abstract: We expect hypersurface singularities that carry a holomorphic  symplectic structure to be a rare phenomenon. If one imposes  natural technical conditions like equivariance of all data with respect to a C*-action with strictly positive weights, the only known hypersurfaces are: 1. ADE-singularities, 2. a series of  4-dimensional examples and 3. a single 6-dimensional exmaple.