Ricci-Flat Metrics on the Complement of Singular Divisors


Yu-Shen Lin (Boston University, USA)
2022-12-30  10:00 - 11:30
Room 202, Astronomy and Mathematics Building


Given a Fano manifold Y ... 00000&s=0&latex=Y" title="Y" width="12" data-bit="iit" /> with a smooth anti-canonical divisor D ... 00000&s=0&latex=D" title="D" width="12" data-bit="iit" />, Tian-Yau solved the corresponding complex Monge-Ampere equation and proved that the complement X=Y\backslash D ... latex=X=Y%5Cbackslash%09D" title="X=Y\backslash D" width="70" data-bit="iit" /> admits complete Ricci-flat metrics. It is little known if X ... 00000&s=0&latex=X" title="X" width="13" data-bit="iit" /> admits a complex Ricci-flat metric if D ... 00000&s=0&latex=D" title="D" width="12" data-bit="iit" /> is a simple normal crossing. In this talk, I will explain the recent work of Collins-Li which gives an affirmative result when \mbox{dim}_{\mathbb{C}}Y\geq 3 ... thbb%7BC%7D%7DY%5Cgeq%093" title="\mbox{dim}_{\mathbb{C}}Y\geq 3" width="78" data-bit="iit" />. I will also give some partial results in dimension two based on a joint work in progress with Collins.