Adiabatic limits of Ricci-flat Kahler metrics
Differential Geometry
2018-04-19 v2
Abstract
We study adiabatic limits of Ricci-flat Kahler metrics on a Calabi-Yau manifold which is the total space of a holomorphic fibration when the volume of the fibers goes to zero. By establishing some new a priori estimates for the relevant complex Monge-Ampere equation, we show that the Ricci-flat metrics collapse (away from the singular fibers) to a metric on the base of the fibration. This metric has Ricci curvature equal to a Weil-Petersson metric that measures the variation of complex structure of the Calabi-Yau fibers. This generalizes results of Gross-Wilson for K3 surfaces to higher dimensions.
Keywords
Cite
@article{arxiv.0905.4718,
title = {Adiabatic limits of Ricci-flat Kahler metrics},
author = {Valentino Tosatti},
journal= {arXiv preprint arXiv:0905.4718},
year = {2018}
}
Comments
26 pages; final version to appear in J. Differential Geom