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

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	INVENTIONES MATHEMATICAE
Publisher:	SPRINGER VERLAG
ISSN:	0020-9910
Date:	1991
Volume:	106
Number:	2
Number of Pages:	26
Page Range:	pp. 217-242
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/22441

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