Contracting exceptional divisors by the Kähler-Ricci flow II

Jian Song, Ben Weinkove

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

We investigate the case of the Kähler-Ricci flow blowing down disjoint exceptional divisors with normal bundle O(-k) to orbifold points. We prove smooth convergence outside the exceptional divisors and global Gromov-Hausdorff convergence. Moreover, we prove a conjecture of the authors by establishing the result that the Gromov-Hausdorff limit coincides with the metric completion of the limiting metric under the flow. This improves and extends the previous work of the authors. We apply this to ℙ1-bundles which are higher-dimensional analogues of the Hirzebruch surfaces. We also consider the case of a minimal surface of general type with only distinct irreducible (-2)-curves and show that solutions to the normalized Kähler-Ricci flow converge in the Gromov-Hausdorff sense to a Kähler-Einstein orbifold.

Original languageEnglish (US)
Pages (from-to)1529-1561
Number of pages33
JournalProceedings of the London Mathematical Society
Volume108
Issue number6
DOIs
StatePublished - Jun 2014

ASJC Scopus subject areas

  • Mathematics(all)

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