Geometric flow, Multiplier ideal sheaves and Optimal destabilizer for a Fano manifold

Abstract

S. K. Donaldson asked whether the lower bound of the Calabi functional is achieved by a sequence the normalized Donaldson-Futaki invariants. We answer the question for the Ricci curvature formalism, in place of the scalar curvature. The principle is that the stability indicator is optimized by the multiplier ideal sheaves of certain weak geodesic ray asymptotic to the geometric flow. We actually prove it in the two case: the inverse Monge-Ampere flow and the Kahler-Ricci flow.

arXiv commentWe modified the proof of the main theorem using monotonicity of the K-energy along the inverse Monge-Ampére flow

References in corpus (8)

• A variational approach to the Yau-Tian-Donaldson conjecture
• On the construction of Nadel multiplier ideal sheaves and the limiting behavior of the Ricci flow
• Space of Ricci flows (II)
• A non-Archimedean approach to K-stability
• Basis log canonical thresholds, local intersection estimates, and asymptotically log del Pezzo surfaces
• Multiplier Ideal Sheaves and the Kähler-Ricci Flow
• Mabuchi Solitons and Relative Ding Stability of Toric Fano Varieties
• The inverse Monge-Ampere flow and applications to Kahler-Einstein metrics

Cited by in corpus (5)

• Optimal destabilization of K-unstable Fano varieties via stability thresholds
• Stability and the deformed Hermitian-Yang-Mills equation
• Tan-concavity property for Lagrangian phase operators and applications to the tangent Lagrangian phase flow
• Entropies in $\mu$-framework of canonical metrics and K-stability, I -- Archimedean aspect: Perelman's W-entropy and $\mu$-cscK metrics
• The Kähler-Ricci flow and quantitative bounds for Donaldson-Futaki invariants of optimal degenerations