Description:

Title: Compactifications and Ricci Flat Metrics of C^n
 
Abstract: I will present some background on a recent paper by Chi Li and Zhengyi Zhou which studies the following two conjectures regarding compactifications and Ricci flat metrics of C^n: 
 
1. If (X, Y) is a pair of complex manifolds such that X\Y is biholomorphic to C^n, then X and Y are isomorphic to projective space of dimension n and n - 1 respectively.
 
2. If g is a complete Ricci flat Kahler metric on C^n that is asymptotic to a cone with smooth link, then g is the standard metric.
 
In particular, Li-Zhou show that conjecture 1 is true provided Y is Kahler, and that conjecture 2 is true in dimension 3, and true in all dimensions assuming Shokurov's minimal discrepancy conjecture.