Geometric flow, Multiplier ideal sheaves and Optimal destabilizer for a Fano manifold
Differential Geometry
2020-01-22 v3 Complex Variables
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.
Keywords
Cite
@article{arxiv.1901.08480,
title = {Geometric flow, Multiplier ideal sheaves and Optimal destabilizer for a Fano manifold},
author = {Tomoyuki Hisamoto},
journal= {arXiv preprint arXiv:1901.08480},
year = {2020}
}
Comments
We modified the proof of the main theorem using monotonicity of the K-energy along the inverse Monge-Amp\'ere flow