THE BRUCE-ROBERTS NUMBER OF A FUNCTION ON A WEIGHTED HOMOGENEOUS HYPERSURFACE

Nuno-Ballesteros, J. J.; Orefice, B.; Tomazella, J. N.

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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

THE BRUCE-ROBERTS NUMBER OF A FUNCTION ON A WEIGHTED HOMOGENEOUS HYPERSURFACE

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Author(s):	Nuno-Ballesteros, J. J. ^[1] ; Orefice, B. ^[2] ; Tomazella, J. N. ^[2] Total Authors: 3
Affiliation:	^[1] Univ Valencia, Dept Geometria & Topol, E-46100 Burjassot - Spain ^[2] Univ Fed Sao Carlos, Dept Matemat, BR-13560905 Sao Carlos, SP - Brazil Total Affiliations: 2
Document type:	Journal article
Source:	QUARTERLY JOURNAL OF MATHEMATICS; v. 64, n. 1, p. 269-280, MAR 2013.
Web of Science Citations:	4
Abstract
Given (X, 0)subset of(C-n, 0) a weighted homogeneous germ of hypersurface with isolated singularity and f:(C-n, 0)->(C, 0) a germ of function finitely determined with respect to X, we show that mu(BR)(X, f)=mu(f)+mu(X, f), where mu(f) and mu(X, f) denote the Milnor numbers of f and of the fiber X boolean AND f(-1)(0), respectively, and mu(BR)(X, f) is the Bruce-Roberts number of f with respect to X. We show that the logarithmic characteristic subvariety LC(X) is Cohen-Macaulay and we get relations between the Bruce-Roberts number and the Euler obstruction. (AU)

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