Existence of complete Kahler Ricci-flat metrics on crepant resolutions
Bianca Santoro
TL;DR
This paper proves the existence of complete Ricci-flat Kähler metrics on crepant resolutions of Calabi-Yau singularities and analyzes their asymptotic behavior in specific cases.
Contribution
It establishes new existence results for Ricci-flat metrics on crepant resolutions and compares their asymptotics to the original Calabi-Yau varieties.
Findings
Existence of complete Ricci-flat Kähler metrics on crepant resolutions.
Asymptotic equivalence of metrics in certain Calabi-Yau cases.
Abstract
In this note, we obtain existence results for complete Ricci-flat Kahler metrics on crepant resolutions of singularities of Calabi-Yau varieties. Furthermore, for certain asymptotically flat Calabi-Yau varieties, we show that the Ricci-flat metric on the resolved manifold has the same asymptotic behavior as the initial variety.
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