Kähler forms for families of Calabi-Yau manifolds

Abstract

Kähler-Einstein metrics for polarized families of Calabi-Yau manifolds define a natural hermitian metric on the relative canonical bundle. The fact that the curvature form is equal to the pull-back of the Weil-Petersson form up to a numerical constant is being used for the construction of a Kähler form on the total space of a given family, whose restriction to the fibers is Ricci flat.

Submitted November 3, 2016. Assumptions for Theorem 1 in v2 somewhat relaxed. Minor changes. Misprints fixed