Limits of Calabi-Yau metrics when the Kahler class degenerates

被引：47

作者：

Tosatti, Valentino

机构：

[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

[2] Morningside Ctr Math, Beijing, Peoples R China

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2009年 / 11卷 / 04期

关键词：

Calabi-Yau manifolds; Ricci-flat metrics; degenerate complex Monge-Ampere equations; K3; SURFACES; RICCI FLOW; MANIFOLDS; CURVATURE; CONE; SINGULARITIES; CONJECTURE; CONSTANT; MODULI; MAP;

D O I：

10.4171/JEMS/165

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the behavior 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.

引用

页码：755 / 776

页数：22

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