Milnor number of a vector field along a subscheme: Applications in desingularization
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.
scientific article; zbMATH DE number 1507788