We study the behavior of families of Ricci-flat Kähler metrics on a projective Calabi-Yau manifold when the Kähler 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.
- Calabi-Yau manifolds
- Degenerate complex Monge-Ampère equations
- Ricci-flat metrics
ASJC Scopus subject areas
- Applied Mathematics