Talks

Ricci-Flat Metrics on the Complement of Singular Divisors

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

 



Given a Fano manifold Yhttps://s0.wp.com/latex.php?zoom=3& ... 00000&s=0&latex=Y" title="Y" width="12" data-bit="iit" /> with a smooth anti-canonical divisor Dhttps://s0.wp.com/latex.php?zoom=3& ... 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 Dhttps://s0.wp.com/latex.php?zoom=3& ... 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 Xhttps://s0.wp.com/latex.php?zoom=3& ... 00000&s=0&latex=X" title="X" width="13" data-bit="iit" /> admits a complex Ricci-flat metric if Dhttps://s0.wp.com/latex.php?zoom=3& ... 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 3https://s0.wp.com/latex.php?zoom=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.