TY - JOUR
T1 - The fundamental group of the complement of the branch curve of the second Hirzebruch surface
AU - Amram, Meirav
AU - Friedman, Michael
AU - Teicher, Mina
N1 - 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”).
PY - 2009/3
Y1 - 2009/3
N2 - 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.
AB - 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.
KW - Braid monodromy
KW - Branch curve
KW - Classification of surfaces
KW - Degeneration
KW - Fundamental group
KW - Generic projection
KW - Hirzebruch surfaces
UR - http://www.scopus.com/inward/record.url?scp=69549124036&partnerID=8YFLogxK
U2 - 10.1016/j.top.2009.03.002
DO - 10.1016/j.top.2009.03.002
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AN - SCOPUS:69549124036
SN - 0040-9383
VL - 48
SP - 23
EP - 40
JO - Topology
JF - Topology
IS - 1
ER -