Speaker : Dr. Hsieh-Yung Lin (Universitaet Bonn)
Title : Some pieces of frontiers between symplectic, Kahler, and algebraic geometry
Time : 2017-09-06 (Wed) 11:00 - 12:30
Place : Seminar Room 638, Institute of Mathematics (NTU Campus)
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?