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arXiv · 1610.03366

The K\"ahler-Ricci flow on Fano bundles

Xin Fu·Shijin Zhang
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Abstract

We study the behavior of the K\"ahler-Ricci flow on some Fano bundle which is a trivial bundle on one Zariski open set. We show that if the fiber is $\mathbb{P}^{m}$ blown up at one point or some weighted projective space blown up at the orbifold point and the initial metric is in a suitable k\"ahler class, then the fibers collapse in finite time and the metrics converge sub-sequentially in Gromov-Hausdorff sense to a metric on the base.

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Xin Fu, Shijin Zhang. 2016-10-11. The K\"ahler-Ricci flow on Fano bundles. https://arxiv.org/abs/1610.03366

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