K\"ahler-Ricci Flow and the Minimal Model Program for Projective Varieties
Algebraic Geometry
2007-05-23 v1 Differential Geometry
Abstract
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.
Cite
@article{arxiv.math/0603064,
title = {K\"ahler-Ricci Flow and the Minimal Model Program for Projective Varieties},
author = {Paolo Cascini and Gabriele La Nave},
journal= {arXiv preprint arXiv:math/0603064},
year = {2007}
}
Comments
16 pages