English

A note on $\xi-$Bergman kernels

Complex Variables 2025-07-15 v2

Abstract

In the present note, we introduce the ξ\xi-complex singularity exponents, which come from the asymptotic property of ξ\xi-Bergman kernels on sub-level sets of plurisubharmonic functions; give some relations (including a closedness property) among ξ\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 ξ\xi-complex singularity exponents.

Keywords

Cite

@article{arxiv.2212.01561,
  title  = {A note on $\xi-$Bergman kernels},
  author = {Shijie Bao and Qi'an Guan and Zheng Yuan},
  journal= {arXiv preprint arXiv:2212.01561},
  year   = {2025}
}

Comments

22 pages. All comments are welcome! We fixed some typos

R2 v1 2026-06-28T07:21:06.544Z