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arXiv · 1201.6403

Hodge theory of cyclic covers branched over a union of hyperplanes

Donu Arapura
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Abstract

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.

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Donu Arapura. 2012-01-30. Hodge theory of cyclic covers branched over a union of hyperplanes. https://doi.org/10.4153/cjm-2013-040-8

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