Hodge Theory of Cyclic Covers Branchedover a Union of Hyperplanes

Arapura, Donu

Canadian journal of mathematics, Tome 66 (2014) no. 3, pp. 505-524

Résumé

Suppose that $Y$ is a cyclic cover of projective space branched over a hyperplane arrangement $D$ and that $U$ is the complement of the ramification locus in $Y$ . The first theorem in this paper implies that the Beilinson–Hodge conjecture holds for $U$ if certain multiplicities of $D$ are coprime to the degree of the cover. For instance, this applies when $D$ is reduced with normal crossings. The second theorem shows that when $D$ has normal crossings and the degree of the cover is a prime number, the generalized Hodge conjecture holds for any toroidal resolution of $Y$ . The last section contains some partial extensions to more general nonabelian covers.

Détail

DOI : 10.4153/CJM-2013-040-8

Mots-clés : 14C30, Hodge cycles, hyperplane arrangements

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