Room 638, Institute of Mathematics, Academia Sinica

(中研院數學所 638室)

Some Pieces of Frontiers between Symplectic, Kähler, and Algebraic Geometry

Hsieh-Yung Lin (Universitaet Bonn)

Abstract:

Here is a foretaste of the kind of frontiers that we will discuss in the talk.

1)

If we forget the complex structure of a Kähler manifold X, we obtain a symplectic manifold. Unlike Kähler manifolds, deforming symplectic manifolds is much more easier. Accordingly many invariants of X coming from its Kähler or algebraic geometry disappear whenever we deform X symplectically. Are there invariants which still survive?

2)

A compact Kähler manifolds X carries an algebraic structure precisely when it can be embedded into a projective space (called projective manifold). This time deforming X as a Kähler manifolds is easier than deforming it as an algebraic variety. Can we obtain every compact Kähler manifold by deforming a projective manifold as a Kähler manifold?