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arXiv · 1003.0718

Contracting exceptional divisors by the K\"ahler-Ricci flow

Jian Song·Ben Weinkove
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Abstract

We give a criterion under which a solution g(t) of the Kahler-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 convergence of g(t) in the sense of Gromov-Hausdorff and smooth convergence away from the exceptional divisors. We call this behavior for the Kahler-Ricci flow a canonical surgical contraction. In particular, our results show that the Kahler-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.

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Jian Song, Ben Weinkove. 2010-03-03. Contracting exceptional divisors by the K\"ahler-Ricci flow. https://doi.org/10.1215/00127094-1962881

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