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Fundamental groups of a class of rational cuspidal plane curves

A. Muhammed Uludağ

Department of Mathematics, Galatasaray University, Çırağan Cad. No. 36, Beşiktaş, 34357 Istanbul, Turkey

E-mail Address: muhammed.uludag@gmail.com

https://doi.org/10.1142/S0129167X16501044Cited by:0 (Source: Crossref)

Abstract

We compute the presentations of fundamental groups of the complements of a class of rational cuspidal projective plane curves classified by Flenner, Zaidenberg, Fenske and Saito. We use the Zariski–Van Kampen algorithm and exploit the Cremona transformations used in the construction of these curves. We simplify and study the group presentations so obtained and determine if they are abelian, finite or big, i.e. if they contain free non-abelian subgroups. We also study the quotients of these groups to some extent.

To Prof. Mikhail Zaidenberg on the Occasion of his 70th Birthday

Keywords:

AMSC: 57M25, 57M27

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