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arXiv:0710.4579 [math.DG]AbstractReferencesReviewsResources

Limits of Calabi-Yau metrics when the Kahler class degenerates

Valentino Tosatti

Published 2007-10-25, updated 2009-04-13Version 5

We study the behaviour of families of Ricci-flat Kahler metrics on a projective Calabi-Yau manifold when the Kahler classes degenerate to the boundary of the ample cone. We prove that if the limit class is big and nef the Ricci-flat metrics converge smoothly on compact sets outside a subvariety to a limit incomplete Ricci-flat metric. The limit can also be understood from algebraic geometry.

Comments: 22 pages; a new L^infty estimate in section 4; to appear in J.Eur.Math.Soc. 2009
Journal: J. Eur. Math. Soc. (JEMS) 11 (2009), no.4, 755-776.
Categories: math.DG, math.AG
Subjects: 32Q25, 14J32, 14J28, 32Q20
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