Metric flips with Calabi ansatz

Abstract

We study the limiting behavior of the Kahler-Ricci flow on $\mathbb{P}({\mathcal{O}}_{{\mathbb{P}}^n}\oplus {\mathcal{O}}_{{\mathbb{P}}^n}(-1{)}^{\oplus (m+1)})$, assuming the initial metric satisfies the Calabi symmetry. We show that the flow either shrinks to a point, collapses to ${\mathbb{P}}^n$ 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.

References in corpus (2)

• Completion of the Proof of the Geometrization Conjecture
• On the construction of Nadel multiplier ideal sheaves and the limiting behavior of the Ricci flow

Cited by in corpus (1)

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