English

Links of singularities of inner non-degenerate mixed functions

Geometric Topology 2025-02-19 v1

Abstract

We introduce the notion of a (strongly) inner non-degenerate mixed function f:C2Cf:\mathbb{C}^2\to\mathbb{C}. We show that inner non-degenerate mixed polynomials have weakly isolated singularities and strongly inner non-degenerate mixed polynomials have isolated singularities. Furthermore, under one additional assumption, which we call "niceness", the links of these singularities can be completely characterized in terms of the Newton boundary of ff. In particular, adding terms above the Newton boundary does not affect the topology of the link. This allows us to define an infinite family of real algebraic links in the 3-sphere.

Keywords

Cite

@article{arxiv.2208.11655,
  title  = {Links of singularities of inner non-degenerate mixed functions},
  author = {Raimundo N. Araújo dos Santos and Benjamin Bode and Eder L. Sanchez Quiceno},
  journal= {arXiv preprint arXiv:2208.11655},
  year   = {2025}
}

Comments

36 pages, 4 figures