The K"ahler-Ricci flow with Log Canonical Singularities

Abstract

We establish the existence of the K"ahler-Ricci flow on projective varieties with log canonical singularities. This generalizes some of the existence results of Song-Tian \cite{ST3} in case of projective varieties with klt singularities. We also prove that the normalized K"ahler-Ricci flow will converge to the \ka-Einstein metric with negative Ricci curvature on semi-log canonical models in the sense of currents. Finally we also construct K"ahler-Ricci flow solutions performing divisorial contractions and flips with log canonical singularities.

arXiv commentCorrection to Lemma 3.1 and Theorem 3.13; detail added to Lemma 6.1 and proof; notation simplified throughout; To appear in International Mathematics Research Notices

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