Journal of the Mathematical Society of Japan

Irreducible plane sextics with large fundamental groups


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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

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

First available in Project Euclid: 6 November 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H30: Coverings, fundamental group [See also 14E20, 14F35]
Secondary: 14H45: Special curves and curves of low genus

plane sextic torus type fundamental group trigonal curve


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

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