Position of singularities and fundamental group of the complement of a union of lines

Fan, Kwai-Man

doi:10.1090/S0002-9939-96-03487-9

Position of singularities and fundamental group of the complement of a union of lines
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Proc. Amer. Math. Soc. 124 (1996), 3299-3303 Request permission

Abstract:

In this paper we give two examples of complex line arrangements in $CP^{2}$ with 7 lines, that both have 3 triple points and 12 double points, and their complements have nonisomorphic global fundamental groups. These two line arrangements are, in some sense, a much simpler example of a pair of plane algebraic curves that have the same local topology but have complements with different global topology—compare with the example given by Zariski, or the recent example given by Artal-Bartolo.

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