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

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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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     author = {Vik. S. Kulikov and V. S. Kulikov},
     title = {On the monodromy and mixed {Hodge} structure on cohomology of the infinite cyclic covering of the complement to a~plane algebraic curve},
     journal = {Izvestiya. Mathematics },
     pages = {367--386},
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     year = {1995},
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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/