Milnor number of a vector field along a subscheme: Applications in desingularization
type: Item
instance of: scholarly article
title: Milnor number of a vector field along a subscheme: Applications in desingularization
zbMATH Open document ID: 0966.32020
author: Fernando Sancho de Salas
published in: Advances in Mathematics
publication date: 2001-08-06T00:00:00Z
review text: The author considers differential equations on regular schemes over a field \(k\) (i.e., a morphism of an invertible sheaf to the tangent sheaf with torsion-free quotient). In [\textit{F. Sancho de Salas} and \textit{P. Sancho de Salas}, Compos. Math. 106, No. 2, 235-246 (1997; Zbl 0889.32036)] the case of absolutely isolated singularities was studied. The Baum-Bott formula for characteristic classes allowed to compute the variation of the Milnor number under blowing up and to prove desingularisation. Using a generalisation of the Kempf-Laksov theorem [\textit{G. Kempf} and \textit{D. Laksov}, Acta Math. 132, 153-162 (1974; Zbl 0295.14023)] these results are here generalised to non-isolated singularities. They apply to the desingularisation of absolutely isolated components of the singular locus of the differential equation.
Mathematics Subject Classification ID: 32S65
zbMATH DE Number: 1507788
zbMATH Keywords: Milnor number
zbMATH Keywords: non-isolated singularities
zbMATH Keywords: desingularisation
reviewed by: Jan Stevens
MaRDI profile type: Publication
full work available at URL: aima.1999.1900
OpenAlex ID: W2085384237
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DOI: 10.1006/AIMA.1999.1900
description: scientific article; zbMATH DE number 1507788