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 language | English |
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Pages (from-to) | 23-40 |
Number of pages | 18 |
Journal | Topology |
Volume | 48 |
Issue number | 1 |
DOIs | |
State | Published - 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”).
Funding
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”).
Funders | Funder number |
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Emmy Noether Research Institute for Mathematics | |
Minerva Foundation of Germany | |
Deutscher Akademischer Austauschdienst | EU-network HPRN-CT-2009-00099 |
Israel Science Foundation | 8008/02-3 |
Keywords
- Braid monodromy
- Branch curve
- Classification of surfaces
- Degeneration
- Fundamental group
- Generic projection
- Hirzebruch surfaces