Tohoku Mathematical Journal
2010
September
SECOND SERIES VOL. 62, NO. 3

Tohoku Math. J.
62 (2010), 329-355

Title PLANE SEXTICS WITH A TYPE $\bold{E}_8$ SINGULAR POINT

Author Alex Degtyarev

(Received April 10, 2009, revised January 6, 2010)
Abstract. We construct explicit geometric models for and compute the fundamental groups of all plane sextics with simple singularities only and with at least one type $\bold{E}_8$ singular point. In particular, we discover four new sextics with nonabelian fundamental groups; two of them are irreducible. The groups of the two irreducible sextics found are finite. The principal tool used is the reduction to trigonal curves and Grothendieck's dessins d'enfants.

2000 Mathematics Subject Classification. Primary 14H45; Secondary 14H30, 14H50.
Key words and phrases. Plane sextic, singular curve, fundamental group, trigonal curve, dessin d'enfant.

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