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 -