Invariants of Combinatorial Line Arrangements and Rybnikov's Example
Algebraic Geometry
2018-05-04 v1 Geometric Topology
Abstract
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.
Cite
@article{arxiv.math/0403543,
title = {Invariants of Combinatorial Line Arrangements and Rybnikov's Example},
author = {E. Artal and J. Carmona and J. I. Cogolludo and M. A. Marco},
journal= {arXiv preprint arXiv:math/0403543},
year = {2018}
}
Comments
27 pages, 2 eps figures