#### Volume 14, issue 1 (2010)

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Plane sextics via dessins d'enfants

### Alex Degtyarev

Geometry & Topology 14 (2010) 393–433
##### 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 ${E}_{7}$ singular point and compute their fundamental groups. All groups found are finite; one of them is nonabelian.

##### Keywords
plane sextic, fundamental group, trigonal curve, dessin d'enfant
##### Mathematical Subject Classification 2000
Primary: 14H45
Secondary: 14H30, 14H50