Kähler-Ricci Flow and the Minimal Model Program for Projective Varieties

Details Kähler-Ricci Flow and the Minimal Model Program for Projective Varieties Kähler-Ricci Flow and the Minimal Model Program for Projective Varieties

2006-03-02

arxiv.org/abs/math/0603064v1

Mathematics

Algebraic Geometry

16 pages

Scientific paper

In this note we propose to show that the K\"ahler-Ricci flow fits naturally within the context of the Minimal Model Program for projective varieties. In particular we show that the flow detects, in finite time, the contraction theorem of any extremal ray and we analyze the singularities of the metric in the case of divisorial contractions for varieties of general type. In case one has a smooth minimal model of general type (i.e., the canonical bundle is nef and big), we show infinite time existence and analyze the singularities.

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