## Tohoku Mathematical Journal

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

Alex Degtyarev

#### 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

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

Digital Object Identifier
doi:10.2748/tmj/1287148615

Mathematical Reviews number (MathSciNet)
MR2742012

Zentralblatt MATH identifier
1206.14055

#### 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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