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On the polar locus of complex analytic morphisms
Journal article

On the polar locus of complex analytic morphisms

Comptes rendus de l'Académie des sciences. Série I. Mathématique, Vol.324(4), pp.439-442
01/02/1997

Abstract

Mathematics Physical Sciences Science & Technology
Let (S, 0) be a normal two-dimensional analytic germ and phi = (f, g) : (S; 0) --> (C-2, 0) be a germ of a finite analytic morphism. We prove that, in a good resolution of (S, 0) in which the total transform of (fg)(-1)(0) has only normal crossings, the strict transform of the polar locus of phi intersects the exceptional curve in some well-defined regions, of which we give a numerical characterization. These results generalize those of [7].

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