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# Hodge Theory of Cyclic Covers Branched over a Union of Hyperplanes

Published:2013-11-04
Printed: Jun 2014
• Donu Arapura,
Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A.
 Format: LaTeX MathJax PDF

## 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.
 Keywords: Hodge cycles, hyperplane arrangements
 MSC Classifications: 14C30 - Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture

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