Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 50, No. 2, pp. 469-482 (2009)

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The fundamental group for the complement of Cayley's singularities

Meirav Amram, Michael Dettweiler, Michael Friedman and Mina Teicher

Einstein Mathematics Institute, Hebrew University, Jerusalem, Israel and Mathematics Department, Bar-Ilan University, Israel, e-mail:,; IWR, Heidelberg University, Germany, e-mail:; Mathematics Department, Bar-Ilan Un iversity, Israel, e-mail: e-mail:

Abstract: Given a singular surface $X$, one can extract information on it by investigating the fundamental group $\pi_1(X - Sing_X)$. However, calculation of this group is non-trivial, but it can be simplified if a certain invariant of the branch curve of $X$ -- called the braid monodromy factorization -- is known. This paper shows, taking the Cayley cubic as an example, how this fundamental group can be computed by using braid monodromy techniques ([M]) and their liftings. This is one of the first examples that uses these techniques to calculate this sort of fundamental group.

[M] Moishezon, B.; Teicher, M.: {\em Braid group technique in complex geometry I. Line arrangements in $\C\P^2$}. Contemp. Math. {\bf 78} (1988), 425--555.

Keywords: singularities, coverings, fundamental groups, surfaces, mapping class group

Classification (MSC2000): 14B05, 14E20, 14H30, 14Q10

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Electronic version published on: 28 Aug 2009. This page was last modified: 28 Jan 2013.

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