Contracting exceptional divisors by the Kähler-Ricci flow II

Details Contracting exceptional divisors by the Kähler-Ricci flow II Contracting exceptional divisors by the Kähler-Ricci flow II

2011-02-09

arxiv.org/abs/1102.1759v1

Mathematics

Differential Geometry

30 pages

Scientific paper

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. This 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.

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