On Deformations of Fano Manifolds

Abstract

In this paper we provide new necessary and sufficient conditions for the existence of Kähler-Einstein metrics on small deformations of a Fano Kähler-Einstein manifold. We also show that the Weil-Petersson metric can be approximated by the Ricci curvatures of the canonical $L^2$ metrics on the direct image bundles. In addition, we describe the plurisubharmonicity of the energy functional of harmonic maps on the Kuranishi space of the deformation of compact Kähler-Einstein manifolds of general type.

A new equivalent condition has been added to Theorem 1.1. In Theorem 1.2, we removed the assumption on the automorphism group which appeared in the previous version

References in corpus (1)

• Deformation of extremal metrics, complex manifolds and the relative Futaki invariant

Cited by in corpus (1)

• A Weil-Petersson Type Metric on the Space of Fano Kaehler-Ricci Solitons