Geometry & Topology

Plane sextics via dessins d'enfants

Alex Degtyarev

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Abstract

We develop a geometric approach to the study of plane sextics with a triple singular point. As an application, we give an explicit geometric description of all irreducible maximal sextics with a type E7 singular point and compute their fundamental groups. All groups found are finite; one of them is nonabelian.

Article information

Source
Geom. Topol., Volume 14, Number 1 (2010), 393-433.

Dates
Received: 22 December 2008
Revised: 2 October 2009
Accepted: 28 September 2009
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732178

Digital Object Identifier
doi:10.2140/gt.2010.14.393

Mathematical Reviews number (MathSciNet)
MR2578307

Zentralblatt MATH identifier
1175.14024

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 fundamental group trigonal curve dessin d'enfant

Citation

Degtyarev, Alex. Plane sextics via dessins d'enfants. Geom. Topol. 14 (2010), no. 1, 393--433. doi:10.2140/gt.2010.14.393. https://projecteuclid.org/euclid.gt/1513732178


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