Abstract
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.
Original language | English |
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Pages (from-to) | 728-745 |
Number of pages | 18 |
Journal | Science in China, Series A: Mathematics |
Volume | 51 |
Issue number | 4 |
DOIs | |
State | Published - Apr 2008 |
Bibliographical note
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)
Funding
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)
Funders | Funder number |
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Israel Science Foundation | 8008/02-3 |
Keywords
- Braid monodromy
- Branch curve
- Classification of surfaces
- Degeneration
- Fundamental group
- Generic projection
- Hirzebruch surfaces