English

Families of ICIS with constant total Milnor number

Algebraic Geometry 2021-04-19 v2

Abstract

We show that a family of isolated complete intersection singularities (ICIS) with constant total Milnor number has no coalescence of singularities. This extends a well known result of Gabrielov, Lazzeri and L\^e for hypersurfaces. We use A'Campo's theorem to see that the Lefschetz number of the generic monodromy of the ICIS is zero when the ICIS is singular. We give a pair applications for families of functions on ICIS which extend also some known results for functions on a smooth variety.

Keywords

Cite

@article{arxiv.2103.07219,
  title  = {Families of ICIS with constant total Milnor number},
  author = {Rafaela Soares de Carvalho and Juan José Nuño-Ballesteros and Bruna Oréfice-Okamoto and João Nivaldo Tomazella},
  journal= {arXiv preprint arXiv:2103.07219},
  year   = {2021}
}