TY - JOUR
T1 - On fundamental groups related to the Hirzebruch surface F1
AU - Friedman, Michael
AU - Teicher, Mina
N1 - Funding Information:
Received June 25, 2006; accepted July 31, 2007 DOI: 10.1007/s11425-007-0148-7 † Corresponding author This work was supported by the Emmy Noether Institute Fellowship (by the Minerva Foundation of Germany) and Israel Science Foundation (Grant No. 8008/02-3)
PY - 2008/4
Y1 - 2008/4
N2 - Given a projective surface and a generic projection to the plane, the braid monodromy factorization (and thus, the braid monodromy type) of the complement of its branch curve is one of the most important topological invariants, stable on deformations. From this factorization, one can compute the fundamental group of the complement of the branch curve, either in ℂ2 or in ℂℙ2. In this article, we show that these groups, for the Hirzebruch surface F 1,(a,b), are almost-solvable. That is, they are an extension of a solvable group, which strengthen the conjecture on degeneratable surfaces.
AB - Given a projective surface and a generic projection to the plane, the braid monodromy factorization (and thus, the braid monodromy type) of the complement of its branch curve is one of the most important topological invariants, stable on deformations. From this factorization, one can compute the fundamental group of the complement of the branch curve, either in ℂ2 or in ℂℙ2. In this article, we show that these groups, for the Hirzebruch surface F 1,(a,b), are almost-solvable. That is, they are an extension of a solvable group, which strengthen the conjecture on degeneratable surfaces.
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=42149127041&partnerID=8YFLogxK
U2 - 10.1007/s11425-007-0148-7
DO - 10.1007/s11425-007-0148-7
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AN - SCOPUS:42149127041
SN - 1006-9283
VL - 51
SP - 728
EP - 745
JO - Science in China, Series A: Mathematics
JF - Science in China, Series A: Mathematics
IS - 4
ER -