The Fundamental Group of a CP^2 Complement of a Branch Curve as an Extension of a Solvable Group by a Symmetric Group

Details The Fundamental Group of a CP^2 Complement of a Branch Curve as an Extension of a Solvable Group by a Symmetric Group The Fundamental Group of a CP^2 Complement of a Branch Curve as an Extension of a Solvable Group by a Symmetric Group

1998-11-18

arxiv.org/abs/math/9811111v1

Mathematics

Algebraic Geometry

24 pages, 6 Postscript figures. To appear in Math. Ann

Scientific paper

The main result in this paper is as follows: Let S be the branch curve (in the projective plan) of a generic projection of a Veronese surface. Then the fundamental group of the complement of S is an extension of a solvable group by a symmetric group. A group with the property mentioned above is ``almost solvable'' in the sense that it contains a solvable normal subgroup of finite index. This raises the question for which families of simply connected algebraic surfaces of general type is the fundamental group of the complement of the branch curve of a generic projection to the complex plane an extension of a solvable group by a symmetric group?

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