On the construction of Nadel multiplier ideal sheaves and the limiting behavior of the Ricci flow

Abstract

In this note we construct Nadel multiplier ideal sheaves using the Ricci flow on Fano manifolds. This extends a result of Phong, Sesum and Sturm. These sheaves, like their counterparts constructed by Nadel for the continuity method, can be used to obtain an existence criterion for Kahler-Einstein metrics.

arXiv commentv2: 1. added details for the case n=1. 2. added some references. v3: minor changes. To appear in Transactions of the American Mathematical Society

References in corpus (4)

• Ricci flow on Kähler-Einstein manifolds
• Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kahler metrics, I
• The logarithmic Sobolev inequality along the Ricci flow
• On energy functionals, Kahler-Einstein metrics, and the Moser-Trudinger-Onofri neighborhood

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• K-stability of Fano varieties: an algebro-geometric approach
• The Kähler-Ricci flow on Hirzebruch surfaces
• Smooth and singular Kahler-Einstein metrics
• A thermodynamical formalism for Monge-Ampere equations, Moser-Trudinger inequalities and Kahler-Einstein metrics
• Basis divisors and balanced metrics
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• Geodesic Rays and Kähler-Ricci Trajectories on Fano Manifolds
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• On sharp lower bounds for Calabi type functionals and destabilizing properties of gradient flows
• Metric flips with Calabi ansatz
• Remarks on Kahler Ricci Flow
• Stability of Kähler-Ricci flow in the space of Kähler metrics
• Multiplier ideal sheaves and the Kähler-Ricci flow on toric Fano manifolds with large symmetry
• Greatest Lower Bounds on Ricci Curvature for Fano $T$-manifolds of Complexity $1$
• Multiplier ideal sheaves and integral invariants on toric Fano manifolds
• On the optimal volume upper bound for Kähler manifolds with positive Ricci curvature (with an appendix by Yuchen Liu)
• K-stability of Gorenstein Fano group compactifications with rank two
• Kähler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII
• Greatest Ricci lower bounds of projective horospherical manifolds of Picard number one