English

Semicontinuity of the {\L}ojasiewicz exponent

Algebraic Geometry 2011-02-24 v1

Abstract

We prove that the {\L}ojasiewicz exponent l0(f)l_0(f) of a finite holomorphic germ f:(Cn,0)(Cn,0)f:(C^n,0)\to(C^n,0) is lower semicontinuous in any multiplicity-constant deformation of ff.

Keywords

Cite

@article{arxiv.1102.4730,
  title  = {Semicontinuity of the {\L}ojasiewicz exponent},
  author = {Arkadiusz Ploski},
  journal= {arXiv preprint arXiv:1102.4730},
  year   = {2011}
}