On the Seifert form at infinity associated with polynomial maps
type: Item
instance of: scholarly article
title: On the Seifert form at infinity associated with polynomial maps
zbMATH Open document ID: 0933.32042
author: András Némethi
published in: Journal of the Mathematical Society of Japan
publication date: 2000-03-26T00:00:00Z
review text: If a polynomial map \(f:{\mathbb C}^n\to {\mathbb C}\) has a nice behaviour at infinity (e.g. it is a ``good polynomial''), then the Milnor fibration at infinity exists; in particular, one can define the Seifert form at infinity \(\Gamma(f)\) associated with \(f\). In this paper we prove a Sebastiani--Thom type formula. Namely, if \(f:{\mathbb C}^n\to {\mathbb C}\) and \(g:{\mathbb C}^m\to {\mathbb C}\) are ``good'' polynomials, and we define \(h=f\oplus g: {\mathbb C}^{n+m}\to {\mathbb C}\) by \(h(x,y)=f(x)+g(y)\), then \(\Gamma(h)=(-1)^{mn} \Gamma(f)\otimes \Gamma(g)\). This is the global analogue of the local result, proved independently by K. Sakamoto and P. Deligne for isolated hypersurface singularities.
reviewed by: András Némethi
Mathematics Subject Classification ID: 32S55
Mathematics Subject Classification ID: 14F45
Mathematics Subject Classification ID: 14L24
Mathematics Subject Classification ID: 57Q45
zbMATH DE Number: 1336908
zbMATH Keywords: good polynomials
zbMATH Keywords: Milnor fibrations at infinity
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/05110063
OpenAlex ID: W1969839761
DOI: 10.2969/JMSJ/05110063
Recommended article: On the geometry of polynomial mappings at infinity
Recommended article: On the monodromy at infinity of a polynomial map, II
Recommended article: Unfolding polynomial maps at infinity
Recommended article: The moduli space of polynomial maps and their fixed-point multipliers
Recommended article: Q4238821
Recommended article: Topological invariants of polynomial maps
Recommended article: Poincaré polynomials of a map and a relative Hilali conjecture
Recommended article: Q3102158
Recommended article: Seifert circles and knot polynomials
Recommended article: An infinite family of homogeneous polynomial self-maps of spheres
description: scientific article; zbMATH DE number 1336908