Links of singularities of inner non-degenerate mixed functions

Fuente: arXiv
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Main Authors: Santos, Raimundo N. Araújo dos, Bode, Benjamin, Quiceno, Eder L. Sanchez
Format: Preprint
Published: 2022
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author Santos, Raimundo N. Araújo dos
Bode, Benjamin
Quiceno, Eder L. Sanchez
author_facet Santos, Raimundo N. Araújo dos
Bode, Benjamin
Quiceno, Eder L. Sanchez
contents We introduce the notion of a (strongly) inner non-degenerate mixed function $f:\mathbb{C}^2\to\mathbb{C}$. 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 $f$. 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.
format Preprint
id arxiv_https___arxiv_org_abs_2208_11655
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Links of singularities of inner non-degenerate mixed functions
Santos, Raimundo N. Araújo dos
Bode, Benjamin
Quiceno, Eder L. Sanchez
Geometric Topology
Primary 32S55, 57K10, Secondary 14M25, 14P05, 14P15, 14P25, 32S05
We introduce the notion of a (strongly) inner non-degenerate mixed function $f:\mathbb{C}^2\to\mathbb{C}$. 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 $f$. 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.
title Links of singularities of inner non-degenerate mixed functions
topic Geometric Topology
Primary 32S55, 57K10, Secondary 14M25, 14P05, 14P15, 14P25, 32S05
url https://arxiv.org/abs/2208.11655