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Fundamental groups of projective discriminant complements

Title data

Lönne, Michael:
Fundamental groups of projective discriminant complements.
In: Duke Mathematical Journal. Vol. 150 (2009) Issue 2 . - pp. 357-405.
ISSN 1547-7398
DOI: https://doi.org/10.1215/00127094-2009-055

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: fundamental group; discriminant complement; presentations
Subject classification: Mathematics Subject Classification Code: 14J70 14D05
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Former Professors > Professorship Algebraic Geometry - apl. Prof. Dr. Michael Lönne
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 24 Nov 2021 07:34
Last Modified: 24 Nov 2021 07:34
URI: https://eref.uni-bayreuth.de/id/eprint/67995