What question did this study set out to answer?

The research aims to explore finite time singularities in the Chern-Ricci flow and their implications.

March 19, 2026Open Access

Singularities of the Chern–Ricci flow

Key Points

The research aims to explore finite time singularities in the Chern-Ricci flow and their implications.
Examined degenerate parabolic complex Monge-Ampere equations.
Started from positive (1,1)-currents in the analysis.
Extended previous work on uniform estimates for degenerate equations.
Applied findings to Chern-Ricci flow in log terminal varieties.
Demonstrated smooth behavior outside specific analytic subsets.
Generalized existing results related to degeneracy and singularities.
Established uniform a priori estimates for complex Monge-Ampere equations.

Abstract

We study the nature of finite time singularities for the Chern-Ricci flow, partially answering a question posed by Tosatti and Weinkove.We show that a solution of degenerate parabolic complex Monge-Ampre equations, starting from arbitrarily positive (1,1)-currents, is smooth outside some analytic subset, generalizing works by Di Nezza and Lu.Moreover, we extend Guedj and Lu's recent approach to establish uniform a priori estimates for degenerate complex Monge-Ampre equations on compact Hermitian manifolds.We apply these results to study the Chern-Ricci flow on log terminal varieties starting from a current with mild singularities.

Bookmark

View Full Paper