Abstract or Additional Information
The purpose of this talk is to discuss some recent general results about symplectic geometry of smooth projective varieties using toric degenerations (motivated by commutative algebra). The main result is the following: Let X be a smooth n-dimensional complex projective variety embedded in a projective space and equipped with a Kähler structure induced from a Fubini-Study Kahler form. We show that for any $\epsilon>0$ the manifold X has an open subset U (in the usual topology) such that $vol(X \setminus U) < \epsilon$ and moreover U is symplectomorphic to the algebraic torus $(\mathbb{C}^*)^n$ equipped with a toric Kahler form.
I will continue with material from last week and give a clear description of the degeneration construction. I will also discuss some applications. I will assume only basic knowledge of complex manifolds and algebraic varieties.