Invariants of Combinatorial Line Arrangements and Rybnikov's Example

Details Invariants of Combinatorial Line Arrangements and Rybnikov's Example Invariants of Combinatorial Line Arrangements and Rybnikov's Example

2004-03-31

arxiv.org/abs/math/0403543v1

Mathematics

Algebraic Geometry

27 pages, 2 eps figures

Scientific paper

Following the general strategy proposed by G.Rybnikov, we present a proof of his well-known result, that is, the existence of two arrangements of lines having the same combinatorial type, but non-isomorphic fundamental groups. To do so, the Alexander Invariant and certain invariants of combinatorial line arrangements are presented and developed for combinatorics with only double and triple points. This is part of a more general project to better understand the relationship between topology and combinatorics of line arrangements.

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