Irreducible plane sextics with large fundamental groups

Details Irreducible plane sextics with large fundamental groups Irreducible plane sextics with large fundamental groups

2007-12-14

arxiv.org/abs/0712.2290v2

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

Mathematics

Algebraic Geometry

A revised version: a few proofs added/clarified

Scientific paper

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.

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