The Kähler-ricci flow on projective bundles

Jian Song; Gábor Székelyhidi; Ben Weinkove

doi:10.1093/imrn/rnr265

The Kähler-ricci flow on projective bundles

Jian Song, Gábor Székelyhidi, Ben Weinkove^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

We study the behavior of the Kähler-Ricci flow on projective bundles. We show that if the initial metric is in a suitable Kähler class, then the fibers collapse in finite time and the metrics converge subsequentially in the Gromov-Hausdorff sense to a metric on the base.

Original language	English (US)
Pages (from-to)	243-257
Number of pages	15
Journal	International Mathematics Research Notices
Volume	2013
Issue number	2
DOIs	https://doi.org/10.1093/imrn/rnr265
State	Published - Jan 1 2013

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Mathematics(all)

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10.1093/imrn/rnr265

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title = "The K{\"a}hler-ricci flow on projective bundles",

abstract = "We study the behavior of the K{\"a}hler-Ricci flow on projective bundles. We show that if the initial metric is in a suitable K{\"a}hler class, then the fibers collapse in finite time and the metrics converge subsequentially in the Gromov-Hausdorff sense to a metric on the base.",

author = "Jian Song and G{\'a}bor Sz{\'e}kelyhidi and Ben Weinkove",

note = "Funding Information: This work was supported in part by an NSF CAREER grant DMS-08-47524 and a Sloan Fellowship (to J.S.) and by the NSF grant DMS-09-04223 (to G.S.), and by the NSF grants DMS-08-48193, DMS-11-05373 and a Sloan Fellowship (to B.W.).",

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AU - Song, Jian

AU - Székelyhidi, Gábor

AU - Weinkove, Ben

N1 - Funding Information: This work was supported in part by an NSF CAREER grant DMS-08-47524 and a Sloan Fellowship (to J.S.) and by the NSF grant DMS-09-04223 (to G.S.), and by the NSF grants DMS-08-48193, DMS-11-05373 and a Sloan Fellowship (to B.W.).

PY - 2013/1/1

Y1 - 2013/1/1

N2 - We study the behavior of the Kähler-Ricci flow on projective bundles. We show that if the initial metric is in a suitable Kähler class, then the fibers collapse in finite time and the metrics converge subsequentially in the Gromov-Hausdorff sense to a metric on the base.

AB - We study the behavior of the Kähler-Ricci flow on projective bundles. We show that if the initial metric is in a suitable Kähler class, then the fibers collapse in finite time and the metrics converge subsequentially in the Gromov-Hausdorff sense to a metric on the base.

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The Kähler-ricci flow on projective bundles

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