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1 November 2009 Fundamental groups of projective discriminant complements
Michael Lönne
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Duke Math. J. 150(2): 357-405 (1 November 2009). DOI: 10.1215/00127094-2009-055

Abstract

We investigate the complement of the discriminant in the projective space PSymdCn+1 of polynomials defining hypersurfaces of degree d in Pn. Following the ideas of Zariski, we are able to give a presentation for the fundamental group of the discriminant complement which generalises the well-known presentation in case n=1 (i.e., of the spherical braid group on d strands).

In particular, our argument proceeds by a geometric analysis of the discriminant polynomial as proposed in [Be] and draws on results and methods from [L1] addressing a comparable problem for any versal unfolding of Brieskorn-Pham singularities

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Michael Lönne. "Fundamental groups of projective discriminant complements." Duke Math. J. 150 (2) 357 - 405, 1 November 2009. https://doi.org/10.1215/00127094-2009-055

Information

Published: 1 November 2009
First available in Project Euclid: 16 October 2009

zbMATH: 1202.14041
MathSciNet: MR2569617
Digital Object Identifier: 10.1215/00127094-2009-055

Subjects:
Primary: 14J70
Secondary: 14D05

Rights: Copyright © 2009 Duke University Press

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Vol.150 • No. 2 • 1 November 2009
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