Contracting exceptional divisors by the K\"ahler-Ricci flow II
Abstract
We investigate the case of the Kahler-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. In addition, we establish 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 P^1-bundles which are higher-dimensional analogues of the Hirzebruch surfaces. In addition, we consider the case of a minimal surface of general type with only distinct irreducible (-2)-curves and show that solutions to the normalized Kahler-Ricci flow converge in the Gromov-Hausdorff sense to a Kahler-Einstein orbifold.
Keywords
Cite
@article{arxiv.1102.1759,
title = {Contracting exceptional divisors by the K\"ahler-Ricci flow II},
author = {Jian Song and Ben Weinkove},
journal= {arXiv preprint arXiv:1102.1759},
year = {2018}
}
Comments
40 pages, v2 includes now a detailed proof of the identification of the GH limit with the metric completion