GÖKOVA GEOMETRY / TOPOLOGY PROCEEDINGS

Published in Proceedings of Gökova Geometry-Topology Conference 2005
Title Ricci-flat deformations of asymptotically cylindrical Calabi–Yau manifolds
Author Alexei Kovalev
Abstract
We study a class of asymptotically cylindrical Ricci-flat Kähler metrics arising on quasiprojective manifolds. Using the Calabi–Yau geometry and analysis and the Kodaira–Kuranishi–Spencer theory and building up on results of N.Koiso, we show that under rather general hypotheses any local asymptotically cylindrical Ricci-flat deformations of such metrics are again Kähler, possibly with respect to a perturbed complex structure. We also find the dimension of the moduli space for these local deformations. In the class of asymptotically cylindrical Ricci-flat metrics on 2n-manifolds, the holonomy reduction to SU(n) is an open condition.
Pages140-156
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Last updated: January 2007
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