Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 50, No. 2, pp. 469-482 (2009)
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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 singularitiesMeirav Amram, Michael Dettweiler, Michael Friedman and Mina TeicherEinstein Mathematics Institute, Hebrew University, Jerusalem, Israel and Mathematics Department, Bar-Ilan University, Israel, e-mail: ameirav@math.huji.ac.il, meirav@macs.biu.ac.il; IWR, Heidelberg University, Germany, e-mail: michael.dettweiler@iwr.uni-heidelberg.de; Mathematics Department, Bar-Ilan Un iversity, Israel, e-mail: fridmam@macs.biu.ac.il e-mail: teicher@macs.biu.ac.ilAbstract: 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 Full text of the article:
Electronic version published on: 28 Aug 2009. This page was last modified: 28 Jan 2013.
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