## Advanced Studies in Pure Mathematics

### On irreducible sextics with non-abelian fundamental group

Alex Degtyarev

#### Abstract

We calculate the fundamental groups $\pi = \pi_1 (\mathbb{P}^2 \smallsetminus B)$ for all irreducible plane sextics $B \subset \mathbb{P}^2$ with simple singularities for which $\pi$ is known to admit a dihedral quotient $\mathbb{D}_{10}$. All groups found are shown to be finite, two of them being of large order: 960 and 21600.

#### Article information

Dates
Revised: 13 June 2008
First available in Project Euclid: 28 November 2018

https://projecteuclid.org/ euclid.aspm/1543448012

Digital Object Identifier
doi:10.2969/aspm/05610065

Mathematical Reviews number (MathSciNet)
MR2604077

Zentralblatt MATH identifier
1193.14037

#### Citation

Degtyarev, Alex. On irreducible sextics with non-abelian fundamental group. Singularities — Niigata–Toyama 2007, 65--91, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05610065. https://projecteuclid.org/euclid.aspm/1543448012