- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:06
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
11
2009
4
Limits of Calabi–Yau metrics when the Kähler class degenerates
Valentino
Tosatti
Harvard University, CAMBRIDGE, UNITED STATES
Calabi–Yau manifolds, Ricci-flat metrics, degenerate complex Monge–Ampère equations
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.
Several complex variables and analytic spaces
Algebraic geometry
General
755
776
10.4171/JEMS/165
http://www.ems-ph.org/doi/10.4171/JEMS/165