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Hodge Theory of Cyclic Covers Branchedover a Union of Hyperplanes

Published online by Cambridge University Press:  20 November 2018

Donu Arapura
Donu Arapura*
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A.. e-mail: dvb@math.purdue.edu
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Abstract

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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.

Keywords

14C30Hodge cycleshyperplane arrangements
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 66 , Issue 3 , 01 June 2014 , pp. 505 - 524
Copyright
Copyright © Canadian Mathematical Society 2014

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