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A sharp effectiveness result of Demaillys strong openness conjecture

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 Added by Qi'an Guan
 Publication date 2017
  fields
and research's language is English
 Authors Qian Guan




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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.



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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.
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