ACC of plc thresholds

In this paper, we define potential log canonical threshold and prove that the set of those thresholds satisfies the ascending chain condition (ACC). We also consider collections of sequences of Fano type varieties and we study their basic properties including boundedness

Adjoint asymptotic multiplier ideal sheaves

In this paper, we initiate the study of a triple $(X,\Delta,D)$ which consists of a pair $(X,\Delta)$ and a polarizing pseudoeffective divisor $D$. The adjoint asymptotic multiplier ideal sheaf $\mathcal{J}(X,\Delta;\lVert D \rVert)$ associated to the triple gives a simultaneous generalization of the multiplier ideal sheaf $\mathcal{J}(D)$ and asymptotic multiplier ideal sheaf $\mathcal{J}(\lVert D \rVert)$. We describe the closed set defined by the ideal sheaf $\mathcal{J}(X,\Delta;\lVert D \rVert)$ in terms of the minimal model program. We also characterize the case where $\mathcal{J}(X,\Delta;\lVert D \rVert)=\mathcal{O}_X$. Lastly, we also prove a Nadel type vanishing theorem of cohomology using $\mathcal{J}(X,\Delta;\lVert D \rVert)$