UNSPECIFIED. (1991) A-CODIMENSION AND THE VANISHING TOPOLOGY OF DISCRIMINANTS. INVENTIONES MATHEMATICAE, 106 (2). pp. 217-242. ISSN 0020-9910

Abstract

Suppose that f: C(n), 0 --> C(p), 0 is finitely A-determined with n greater-than-or-equal-to p. We define a "Milnor fiber" for the discriminant of f; it is the discriminant of a "stabilization" of f. We prove that this "discriminant Milnor fiber" has the homotopy type of a wedge of spheres of dimension p - 1, whose number we denote by mu-DELTA(f). One of the main theorems of the paper is a "mu = tau" type result: if (n, p) is in the range of nice dimensions in the sense of Mather, then mu-DELTA(f) greater-than-or-equal-to A(e)-codim(f), with equality if f is weighted homogeneous. Outside the nice dimensions we obtain analogous formulae with correction terms measuring the presence of unstable but topologically stable germs in the stabilization. These results are further extended to nonlinear sections of free divisors.

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