Limits of Calabi-Yau metrics when the Kahler class degenerates

被引：46
|
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.
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页码：755 / 776
页数：22
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