Kodai Mathematical Journal

On the geometry of certain irreducible non-torus plane sextics

Christophe Eyral and Mutsuo Oka

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An irreducible non-torus plane sextic with simple singularities is said to be special if its fundamental group factors to a dihedral group. There exist (exactly) ten configurations of simple singularities that are realizable by such curves. Among them, six are realizable by non-special sextics as well. We conjecture that for each of these six configurations there always exists a non-special curve whose fundamental group is abelian, and we prove this conjecture for three configurations (another one has already been treated in one of our previous papers). As a corollary, we obtain new explicit examples of Alexander-equivalent Zariski pairs of irreducible sextics.

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Kodai Math. J., Volume 32, Number 3 (2009), 404-419.

First available in Project Euclid: 11 November 2009

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Eyral, Christophe; Oka, Mutsuo. On the geometry of certain irreducible non-torus plane sextics. Kodai Math. J. 32 (2009), no. 3, 404--419. doi:10.2996/kmj/1257948886. https://projecteuclid.org/euclid.kmj/1257948886

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