Adiabatic limits of Ricciflat Kahler metrics
Abstract
We study adiabatic limits of Ricciflat Kahler metrics on a CalabiYau 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 MongeAmpere equation, we show that the Ricciflat metrics collapse (away from the singular fibers) to a metric on the base of the fibration. This metric has Ricci curvature equal to a WeilPetersson metric that measures the variation of complex structure of the CalabiYau fibers. This generalizes results of GrossWilson for K3 surfaces to higher dimensions.
 Publication:

arXiv eprints
 Pub Date:
 May 2009
 DOI:
 10.48550/arXiv.0905.4718
 arXiv:
 arXiv:0905.4718
 Bibcode:
 2009arXiv0905.4718T
 Keywords:

 Mathematics  Differential Geometry;
 32Q25;
 14J32;
 32Q20;
 53C25
 EPrint:
 26 pages