Contracting exceptional divisors by the K\"ahler-Ricci flow
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.
Keywords
Cite
@article{arxiv.1003.0718,
title = {Contracting exceptional divisors by the K\"ahler-Ricci flow},
author = {Jian Song and Ben Weinkove},
journal= {arXiv preprint arXiv:1003.0718},
year = {2019}
}
Comments
39 pages, v2 minor corrections; v3 due to a gap in the previous argument of Section 3, the assertion that the G-H limit coincides with the metric completion has been removed