Revista Matemática Iberoamericana

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Volume 30, Issue 1, 2014, pp. 25–64
DOI: 10.4171/RMI/768

Published online: 2014-03-23

The Alexander module of a trigonal curve

Alex Degtyarev[1]

(1) Bilkent University, Ankara, Turkey

We describe the Alexander modules and Alexander polynomials (both over $\mathbb{Q}$ and over finite fields $\mathbb{F}_p$) of generalized trigonal curves. The rational case is completely resolved; in the case of characteristic $p>0$, a few points remain open. The results obtained apply as well to plane curves with deep singularities.

Keywords: Trigonal curve, fundamental group, Alexander module, Alexander polynomial, Burau representation, modular group

Degtyarev Alex: The Alexander module of a trigonal curve. Rev. Mat. Iberoam. 30 (2014), 25-64. doi: 10.4171/RMI/768