Degeneration of Kähler-Ricci solitons

Details Degeneration of Kähler-Ricci solitons Degeneration of Kähler-Ricci solitons

2010-06-08

arxiv.org/abs/1006.1577v1

Mathematics

Differential Geometry

24 pages

Scientific paper

Let $(Y, d)$ be a Gromov-Hausdorff limit of $n$-dimensional closed shrinking K\"ahler-Ricci solitons with uniformly bounded volumes and Futaki invariants. We prove that off a closed subset of codimension at least 4, Y is a smooth manifold satisfying a shrinking K\"ahler-Ricci soliton equation. A similar convergence result for K\"ahler-Ricci flow of positive first Chern class is also obtained.

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