The K\"ahler-Ricci flow on Fano bundles

Xin Fu; Shijin Zhang

The K\"ahler-Ricci flow on Fano bundles

Differential Geometry 2016-12-08 v2

Authors: Xin Fu , Shijin Zhang

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.

Keywords

Kähler-Ricci flow Fano bundle metric collapse Gromov-Hausdorff convergence blow-up orbifold

Cite

@article{arxiv.1610.03366,
  title  = {The K\"ahler-Ricci flow on Fano bundles},
  author = {Xin Fu and Shijin Zhang},
  journal= {arXiv preprint arXiv:1610.03366},
  year   = {2016}
}

Comments

Rewrite some part of the introduction, add more references, and correct the computation in the proof of Lemma 2.2. Welcome any Comments. arXiv admin note: text overlap with arXiv:1003.0718 by other authors

The K\"ahler-Ricci flow on Fano bundles

Abstract

Keywords

Cite

Comments

Related papers