Geodesic
On the monodromy and mixed Hodge structure on cohomology of the infinite cyclic covering of the complement to a plane algebraic curve
Izvestiya. Mathematics, Tome 59 (1995) no. 2, pp. 367-386 
Vik. S. Kulikov; V. S. Kulikov. On the monodromy and mixed Hodge structure on cohomology of the infinite cyclic covering of the complement to a plane algebraic curve. Izvestiya. Mathematics, Tome 59 (1995) no. 2, pp. 367-386. http://geodesic.mathdoc.fr/item/IM2_1995_59_2_a6/
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     title = {On the monodromy and mixed {Hodge} structure on cohomology of the infinite cyclic covering of the complement to a~plane algebraic curve},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The semisimplicity is proved of the Alexander automorphism (the monodromy operator) on the cohomology $H^1(X_\infty)_{\ne 1}$ of the infinite cyclic covering of the complement to a plane non-reduced algebraic curve, and, in particular, the semisimplicity of $H^1(X_\infty)$ in the case of an irreducible curve. A natural mixed Hodge structure on $H^1(X_\infty)$ is introduced and the irregularity of cyclic coverings of $P^2$ is calculated in terms of the number of roots of the Alexander polynomial of the branch curve.

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