Multiplier Ideal Sheaves and the K\"ahler-Ricci Flow
D.H. Phong, Natasa Sesum, Jacob Sturm
TL;DR
This paper explores how multiplier ideal sheaves serve as obstructions to the convergence of the K"ahler-Ricci flow on Fano manifolds, utilizing recent analytical estimates to deepen understanding.
Contribution
It introduces a new perspective on the role of multiplier ideal sheaves in the convergence analysis of the K"ahler-Ricci flow, building on previous constructions and recent estimates.
Findings
Multiplier ideal sheaves obstruct K"ahler-Ricci flow convergence.
Recent estimates of Kolodziej and Perelman are instrumental.
Provides a framework linking algebraic and differential geometry.
Abstract
Multiplier ideal sheaves are constructed as obstructions to the convergence of the K\"ahler-Ricci flow on Fano manifolds, following earlier constructions of Kohn, Siu, and Nadel, and using the recent estimates of Kolodziej and Perelman
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory