Fundamental groups of Tangent Conic-Line arrangements with Singularities up to order 6

Details Fundamental groups of Tangent Conic-Line arrangements with Singularities up to order 6 Fundamental groups of Tangent Conic-Line arrangements with Singularities up to order 6

2003-05-29

arxiv.org/abs/math/0305418v4

Mathematics

Geometric Topology

40 pages, many eps figures; Some updates for final version. To appear in Math. Zeit

Scientific paper

We list all the possible fundamental groups of the complements of real conic-line arrangements with two conics which are tangent to each other at two points, with up to two additional lines. For the computations we use the topological local braid monodromies and the techniques of Moishezon-Teicher and van-Kampen. We also include some conjectures concerning the connection between the presentation of the fundamental group of the complements and the geometry of an interesting family of conic line arrangements.

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