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
Publication
Received: 22 December 2008
Revised: 2 October 2009
Accepted: 28 September 2009
Preview posted: 29 October 2009
Published: 2 January 2010
Proposed: Joan Birman
Seconded: Simon Donaldson, Walter Neumann
Authors
 Alex Degtyarev Department of Mathematics Bilkent University 06800 Ankara Turkey http://www.fen.bilkent.edu.tr/~degt