On the incompleteness of the Weil-Petersson metric along degenerations of Calabi-Yau manifolds

Abstract

The classical Weil-Petersson metric on the Teichmüller space of compact Riemann surfaces is a Kähler metric, which is complete only in the case of elliptic curves [Wo]. It has a natural generalization to the deformation spaces of higher dimansional polarized Kähler-Einstein