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A note on $\xi-$Bergman kernels

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arxiv 2212.01561 v2 pith:U3XOUKBP submitted 2022-12-03 math.CV

Shijie Bao , Qi'an Guan , Zheng Yuan This is my paper · ORCID
classification math.CV
keywords complexexponentssingularitypropertybergmankernelsnotesome
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abstract

In the present note, we introduce the $\xi-$complex singularity exponents, which come from the asymptotic property of $\xi-$Bergman kernels on sub-level sets of plurisubharmonic functions; give some relations (including a closedness property) among $\xi-$complex singularity exponents, complex singularity exponents, and jumping numbers; generalize some properties of complex singularity exponents (such as the restriction formula and subadditivity property) to $\xi-$complex singularity exponents.

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  1. Analytic Bertini theorem II --- The local case

    math.AG 2026-07 accept novelty 8.0 of 10

    The local analytic Bertini theorem holds: multiplier ideal sheaves of psh functions on polydisc products restrict to fibers outside a pluripolar set.

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