Plane sextics via dessins d’enfants

Degtyarev, Alex

doi:10.2140/gt.2010.14.393

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Plane sextics via dessins d'enfants

Alex Degtyarev

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 $E_{7}$ 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

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

Alex Degtyarev
Department of Mathematics Bilkent University 06800 Ankara Turkey
http://www.fen.bilkent.edu.tr/~degt

Volume 14, issue 1 (2010)