Plane sextics with a type e8 singular point
Author
Degtyarev, A.
Date
2010Source Title
Tohoku Mathematical Journal
Print ISSN
0040-8735
Electronic ISSN
2186-585X
Publisher
Tohoku Daigaku Suugaku Kyoshitsu
Volume
62
Pages
329 - 355
Language
English
Type
ArticleItem Usage Stats
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Abstract
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 E8 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.