We construct explicit geometric models for and compute the fundamental groups of all plane sextics with simple
singularities only and with at least one type $\bold{E}_8$ singular point. In particular, we discover four new
sextics with nonabelian fundamental groups; two of them are irreducible. The groups of the two irreducible
sextics found are finite. The principal tool used is the reduction to trigonal curves and Grothendieck's
dessins d'enfants.
Publié le : 2010-05-15
Classification:
Plane sextic,
singular curve,
fundamental group,
trigonal curve,
dessin d'enfant,
14H45,
14H30,
14H50
@article{1287148615,
author = {Degtyarev, Alex},
title = {Plane sextics with a type $\bold{E}\_8$ singular point},
journal = {Tohoku Math. J. (2)},
volume = {62},
number = {1},
year = {2010},
pages = { 329-355},
language = {en},
url = {http://dml.mathdoc.fr/item/1287148615}
}
Degtyarev, Alex. Plane sextics with a type $\bold{E}_8$ singular point. Tohoku Math. J. (2), Tome 62 (2010) no. 1, pp. 329-355. http://gdmltest.u-ga.fr/item/1287148615/