## Journal of the Mathematical Society of Japan

### Irreducible plane sextics with large fundamental groups

Alex DEGTYAREV

#### Abstract

We compute the fundamental group of the complement of each irreducible sextic of weight eight or nine (in a sense, the largest groups for irreducible sextics), as well as of 169 of their derivatives (both of and not of torus type). We also give a detailed geometric description of sextics of weight eight and nine and of their moduli spaces and compute their Alexander modules; the latter are shown to be free over an appropriate ring.

#### Article information

Source
J. Math. Soc. Japan, Volume 61, Number 4 (2009), 1131-1169.

Dates
First available in Project Euclid: 6 November 2009

https://projecteuclid.org/euclid.jmsj/1257520503

Digital Object Identifier
doi:10.2969/jmsj/06141131

Mathematical Reviews number (MathSciNet)
MR2588507

Zentralblatt MATH identifier
1183.14040

Subjects
Secondary: 14H45: Special curves and curves of low genus

#### Citation

DEGTYAREV, Alex. Irreducible plane sextics with large fundamental groups. J. Math. Soc. Japan 61 (2009), no. 4, 1131--1169. doi:10.2969/jmsj/06141131. https://projecteuclid.org/euclid.jmsj/1257520503

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