A Numerical Criterion for K-Energy maps of Algebraic Manifolds

Abstract

Let X be a projective manifold. We prove that the Mabuchi Energy of X is bounded below on all degenerations in B (the space of Bergman metrics) if and only if it is bounded below uniformly on B.

arXiv comment8 pages

References in corpus (1)

• CM Stability of Projective varieties

Cited by in corpus (6)

• Space of Ricci flows (II)
• Regularity of Kähler-Ricci flows on Fano manifolds
• K-stability implies CM-stability
• A criterion for the properness of the K-energy in a general Kahler class
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• Discriminants and Higher K-energies on Polarized Kähler Manifolds