Contracting exceptional divisors by the Kähler-Ricci flow

Jian Song*, Ben Weinkove

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

Abstract

We give a criterion under which a solution g.(t) of the Kähler-Ricci flow contracts exceptional divisors on a compact manifold and can be uniquely continued on a new manifold. As t tends to the singular time T from each direction, we prove the convergence of g.(t) in the sense of Gromov-Hausdorff and smooth convergence away from the exceptional divisors. We call this behavior for the Kähler-Ricci flow a canonical surgical contraction. In particular, our results show that the Kähler-Ricci flow on a projective algebraic surface will perform a sequence of canonical surgical contractions until, in finite time, either the minimal model is obtained, or the volume of the manifold tends to zero.

Original languageEnglish (US)
Pages (from-to)367-415
Number of pages49
JournalDuke Mathematical Journal
Volume162
Issue number2
DOIs
StatePublished - Feb 1 2013

ASJC Scopus subject areas

  • Mathematics(all)

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