The fundamental group of the complement of the branch curve of the second Hirzebruch surface

Meirav Amram, Michael Friedman, Mina Teicher

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Abstract

In this paper we prove that the Hirzebruch surface F2, (2, 2) embedded in C P17 supports the conjecture on the structure and properties of fundamental groups of complement of branch curves of generic projections, as laid out in [M. Teicher, New Invariants for surfaces, Contemp. Math. 231 (1999) 271-281]. We use the regeneration from [M. Friedman, M. Teicher, The regeneration of a 5-point, Pure and Applied Mathematics Quarterly 4 (2) (2008) 383-425. Fedor Bogomolov special issue, part I], the van Kampen theorem and properties of over(B, ̃)n-groups [M. Teicher, On the quotient of the braid group by commutators of transversal half-twists and its group actions, Topology Appl. 78 (1997) 153-186], where over(B, ̃)n is a quotient of the braid group Bn, for n = 16.

Original languageEnglish
Pages (from-to)23-40
Number of pages18
JournalTopology
Volume48
Issue number1
DOIs
StatePublished - Mar 2009

Bibliographical note

Funding Information:
This work was partially supported by DAAD and EU-network HPRN-CT-2009-00099 (EAGER); The Emmy Noether Research Institute for Mathematics and the Minerva Foundation of Germany; The Israel Science Foundation grant # 8008/02-3 (Excellency Center “Group Theoretic Methods in the Study of Algebraic Varieties”).

Keywords

  • Braid monodromy
  • Branch curve
  • Classification of surfaces
  • Degeneration
  • Fundamental group
  • Generic projection
  • Hirzebruch surfaces

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