McKernan's stronger ACC conjecture for interpolated lc thresholds

Let (X,B)(X,B) be a pair of dimension dd, let F\mathcal{F} be a foliation on XX, and write B=Bninv+BinvB=B^{\operatorname{ninv}}+B^{\operatorname{inv}} so that (X,F,Bninv)(X,\mathcal{F},B^{\operatorname{ninv}}) is a foliated triple. McKernan's stronger ACC conjecture. For every positive integer dd and DCC set Γ[0,1]\Gamma\subset[0,1], there is an ACC set Γ\Gamma' such that

sup{t[0,1](X,F,Bninv+(1t)Binv,t) is lc}Γ.\sup\{t\in[0,1]\mid (X,\mathcal{F},B^{\operatorname{ninv}}+(1-t)B^{\operatorname{inv}},t)\text{ is lc}\}\in\Gamma'.

The conjecture is proposed as a more general form of McKernan's ACC conjecture and remains open, including in dimension two.

Sources & referencesView supporting material

Primary source

Paolo Cascini, Jingjun Han, Jihao Liu, Fanjun Meng, Calum Spicer, Roberto Svaldi and Lingyao Xie, “Minimal model program for algebraically integrable adjoint foliated structures”, arXiv:2408.14258 (2024).

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