Symplectic Geometry Seminar

Naichung Conan Leung

University of Minnesota

Lagrangian submanifolds in HyperKahler

manifolds, Legendre transformation

 Abstract:

We develop the foundation of the complex symplectic geometry of Lagrangian subvarieties in a hyperkahler manifold. We establish a characterization,a Chern number inequality, topological and geometrical properties of Lagrangian submanifolds. We discuss a category of Lagrangian subvarieties and its relationship with the theory of Lagrangian intersection. We also introduce and study extensively a normalized Legendre transformation of Lagrangian subvarieties under a birational transformation of projective hyperkahler manifolds. We give a Plucker type formula for Lagrangian intersections under this transformation.

 Wednesday, April 24

10:00 a.m.

405 Mathematics