Metric flips with Calabi ansatz

2010/11/07 by Jian Song, Yuan Yuan, Song, Jian +1 · 1 citation
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1011.1608

Abstract

We study the limiting behavior of the Kahler-Ricci flow on ℙ(O_ℙⁿ ⊕ O_ℙⁿ(-1)^{⊕ (m+1)}), assuming the initial metric satisfies the Calabi symmetry. We show that the flow either shrinks to a point, collapses to ℙⁿ or contracts a subvariety of codimension m+1 in Gromov-Hausdorff sense. We also show that the Kahler-Ricci flow resolves certain type of conical singularities in Gromov-Hausdorff sense.

Cited by

• Continuity of Extremal Transitions and Flops for Calabi-Yau Manifolds

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