English

The K"ahler-Ricci flow with Log Canonical Singularities

Differential Geometry 2022-07-14 v3

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.

Keywords

Cite

@article{arxiv.1906.04343,
  title  = {The K"ahler-Ricci flow with Log Canonical Singularities},
  author = {Albert Chau and Huabin Ge and Ka-Fai Li and Liangming Shen},
  journal= {arXiv preprint arXiv:1906.04343},
  year   = {2022}
}

Comments

Correction 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