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.

v2: 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 (3)

• 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
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• Ricci flow on Orbifold
• 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
• Multiplier ideal sheaves and integral invariants on toric Fano manifolds
• 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