The Fundamental Group of the Complement of the Branch Curve of the Hirzebruch Surface
نویسندگان
چکیده
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 ([10]), stable on deformations. From this factorization, one can compute the fundamental group of the complement of the branch curve, either in C or in CP. In this article, we show that these groups, for the Hirzebruch surface F1,(a,b), are almost-solvable. That is they are an extension of a solvable group, which strengthen the conjecture on degeneratable surfaces (see [13]). keywords:Hirzebruch surfaces, degeneration, generic projection, branch curve, braid monodromy, fundamental group, classification of surfaces. AMS classification numbers: 14D05, 14D06, 14E25, 14H30, 14J10, 14Q05, 14Q10.
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