Geometry & Topology 14 (2010) 393–433

DOI: 10.2140/gt.2010.14.393

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.

Keywords

plane sextic, fundamental group, trigonal curve, dessin d'enfant

Mathematical Subject Classification

Primary: 14H45

Secondary: 14H30, 14H50

References

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