In this article, we establish a sharp effectiveness result of Demaillys strong openness conjecture. We also establish a sharp effectiveness result related to a conjecture posed by Demailly and Kollar.
In this note, we reveal that our solution of Demaillys strong openness conjecture implies a matrix version of the conjecture; our solutions of two conjectures of Demailly-Koll{a}r and Jonsson-Mustatu{a} implies the truth of twist
In the present article, we obtain an optimal support function of weighted $L^2$ integrations on superlevel sets of weights of multiplier ideal sheaves, which implies the strong openness property of multiplier ideal sheaves.
If F is an infinitely differentiable function whose composition with a blowing-up belongs to a Denjoy-Carleman class C_M (determined by a log convex sequence M=(M_k)), then F, in general, belongs to a larger shifted class C_N, where N_k = M_2k; i.e., there is a loss of regularity. We show that this loss of regularity is sharp. In particular, loss of regularity of Denjoy-Carleman classes is intrinsic to arguments involving resolution of singularities.