English

On the relative Kuo condition and the second relative Kuo condition

Algebraic Geometry 2020-04-08 v1

Abstract

The Kuo condition and the the second Kuo condition are known as criteria for an r-jet to be V-sufficient in C^r mappings and C^{r+1} mappings, respectively. In a previous paper we considered the notions of V-sufficiency of jets and these Kuo conditions in the relative case to a given closed set, and showed that the relative Kuo condition is a criterion for a relative r-jet to be V-sufficient in C^r mappings and the second relative Kuo condition is a sufficient condition for a relative r-jet to be V-sufficient in C^{r+1} mappings. In this paper we discuss several conditions equivalent to the relative Kuo condition or the second relative Kuo condition.

Cite

@article{arxiv.2004.02880,
  title  = {On the relative Kuo condition and the second relative Kuo condition},
  author = {Karim Bekka and Satoshi Koike},
  journal= {arXiv preprint arXiv:2004.02880},
  year   = {2020}
}

Comments

11 pages, no figure. arXiv admin note: substantial text overlap with arXiv:1703.07069

R2 v1 2026-06-23T14:41:36.396Z