Metric flips with Calabi ansatz

Jian Song; Yuan Yuan

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arXiv · 1011.1608

Metric flips with Calabi ansatz

Jian Song·Yuan Yuan

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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.

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Jian Song, Yuan Yuan. 2010-11-07. Metric flips with Calabi ansatz. https://arxiv.org/abs/1011.1608

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