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Ricci-flat metrics on the canonical bundles

Umar Shahzad
Institution: 
SISSA
Schedule: 
Thursday, April 29, 2021 - 16:30
Location: 
Online
Abstract: 

In many cases, a crepant resolution of $\mathbb{C}^3/G$, where $G$ is a finite subgroup of  $SL(3,\mathbb{C})$, happens to be the total space of the canonical bundle over a Kahler manifold of complex dimension $2$. Since any such crepant resolution is a noncompact Calabi-Yau, there is a natural question of constructing a Ricci-flat metric on it. The existence of such metrics was proven by Joyce. In this talk, I will show how to construct a Ricci-flat metric when a crepant resolution is a space $X=tot(K_{M})$, where $K_{M}$ is the canonical bundle over a 2-dimensional Kahler manifold $M$.  

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