Topology of complex polynomials via polar curves
type: Item
instance of: scholarly article
title: Topology of complex polynomials via polar curves
zbMATH Open document ID: 0939.32027
author: Pi. Cassou-Noguès
author: Alexandru Dimca
published in: Kodai Mathematical Journal
publication date: 1999-09-07T00:00:00Z
review text: The authors consider the global polar curves associated with an affine smooth hypersurface \(F\) in \(\mathbb{C}^n\). If \(f\in \mathbb{C}[x_1, \dots,x_n]\) is a polynomial such that the fiber \(F_t:= f^{-1}(t)\) is smooth and connected, the main result computes the Euler characteristic \(\chi(F_t)\) of \(F_t\) in terms of the polar invariants of the intersections \(F_t\cap E^k\), where \(E^k\) is a general linear subspace of \(\mathbb{C}^n\) of codimension \(k\), \(k=0,1, \dots,n-1\).
reviewed by: Viorel Vâjâitu
Mathematics Subject Classification ID: 32S50
Mathematics Subject Classification ID: 32C18
Mathematics Subject Classification ID: 32A17
zbMATH DE Number: 1333304
zbMATH Keywords: polar variety
zbMATH Keywords: Euler characteristic
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138043993
OpenAlex ID: W2015731925
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DOI: 10.2996/KMJ/1138043993
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description: scientific article; zbMATH DE number 1333304