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1. CJM 2013 (vol 66 pp. 505)

Arapura, Donu
 Hodge Theory of Cyclic Covers Branched over a Union of Hyperplanes 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 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. Keywords:Hodge cycles, hyperplane arrangementsCategory:14C30
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