The ACSS–F-dlt equivalence conjecture for generalized foliated quadruples

Let (X,F,B,M)(X,\mathcal{F},B,\mathbf{M}) be a generalized foliated quadruple. Here ACSS denotes the technical condition defined in the source, and F-dlt denotes foliated divisorial log terminal. ACSS–F-dlt equivalence conjecture. Then (X,F,B,M)(X,\mathcal{F},B,\mathbf{M}) is F-dlt if and only if it is ACSS. This would identify ACSS with F-dlt; the source notes that Q\mathbb{Q}-factorial F-dlt foliated triples are known to be ACSS, while the converse is conjectural.

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Primary source

Guodu Chen, Jingjun Han, Jihao Liu and Lingyao Xie, “Minimal model program for algebraically integrable foliations and generalized pairs”, arXiv:2309.15823 (2026).

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