## Journal of the Mathematical Society of Japan

### Calabi-Yau structures and Einstein-Sasakian structures on crepant resolutions of isolated singularities

Ryushi GOTO

#### Abstract

Let X0 be an affine variety with only normal isolated singularity at p. We assume that the complement X0 \ {p} is biholomorphic to the cone C(S) of an Einstein-Sasakian manifold S of real dimension 2n − 1. If there is a resolution of singularity π: XX0 with trivial canonical line bundle KX, then there is a Ricci-flat complete Kähler metric for every Kähler class of X. We also obtain a uniqueness theorem of Ricci-flat conical Kähler metrics in each Kähler class with a certain boundary condition. We show there are many examples of Ricci-flat complete Kähler manifolds arising as crepant resolutions.

#### Article information

Source
J. Math. Soc. Japan, Volume 64, Number 3 (2012), 1005-1052.

Dates
First available in Project Euclid: 24 July 2012

https://projecteuclid.org/euclid.jmsj/1343133753

Digital Object Identifier
doi:10.2969/jmsj/06431005

Mathematical Reviews number (MathSciNet)
MR2965437

Zentralblatt MATH identifier
1262.53041

#### Citation

GOTO, Ryushi. Calabi-Yau structures and Einstein-Sasakian structures on crepant resolutions of isolated singularities. J. Math. Soc. Japan 64 (2012), no. 3, 1005--1052. doi:10.2969/jmsj/06431005. https://projecteuclid.org/euclid.jmsj/1343133753

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