Tohoku Mathematical Journal

Plane sextics with a type $\bold{E}_8$ singular point

Alex Degtyarev

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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.

Article information

Tohoku Math. J. (2), Volume 62, Number 3 (2010), 329-355.

First available in Project Euclid: 15 October 2010

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Zentralblatt MATH identifier

Primary: 14H45: Special curves and curves of low genus
Secondary: 14H30: Coverings, fundamental group [See also 14E20, 14F35] 14H50: Plane and space curves

Plane sextic singular curve fundamental group trigonal curve dessin d'enfant


Degtyarev, Alex. Plane sextics with a type $\bold{E}_8$ singular point. Tohoku Math. J. (2) 62 (2010), no. 3, 329--355. doi:10.2748/tmj/1287148615.

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