Tohoku Mathematical Journal

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

Alex Degtyarev

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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.

Article information

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

Dates
First available in Project Euclid: 15 October 2010

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1287148615

Digital Object Identifier
doi:10.2748/tmj/1287148615

Mathematical Reviews number (MathSciNet)
MR2742012

Zentralblatt MATH identifier
1206.14055

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

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

Citation

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. https://projecteuclid.org/euclid.tmj/1287148615


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