Article contents
Hodge Theory of Cyclic Covers Branchedover a Union of Hyperplanes
Published online by Cambridge University Press: 20 November 2018
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 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.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 2014
References
- 1
- Cited by