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arXiv · 2305.16461

Singularities of the Chern-Ricci flow

Quang-Tuan Dang
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Abstract

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

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Quang-Tuan Dang. 2025-04-22. Singularities of the Chern-Ricci flow. https://doi.org/10.2140/apde.2026.19.449

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