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Singularities of the Chern-Ricci flow (2305.16461v2)
Published 25 May 2023 in math.DG and math.CV
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-Amp`ere 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-Amp`ere equations on compact Hermitian manifolds. We apply it to studying the Chern-Ricci flows on complex log terminal varieties starting from an arbitrary current.