Hodge Theory of Cyclic Covers Branchedover a Union of Hyperplanes
Canadian journal of mathematics, Tome 66 (2014) no. 3, pp. 505-524
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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.
Arapura, Donu. Hodge Theory of Cyclic Covers Branchedover a Union of Hyperplanes. Canadian journal of mathematics, Tome 66 (2014) no. 3, pp. 505-524. doi: 10.4153/CJM-2013-040-8
@article{10_4153_CJM_2013_040_8,
author = {Arapura, Donu},
title = {Hodge {Theory} of {Cyclic} {Covers} {Branchedover} a {Union} of {Hyperplanes}},
journal = {Canadian journal of mathematics},
pages = {505--524},
year = {2014},
volume = {66},
number = {3},
doi = {10.4153/CJM-2013-040-8},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-040-8/}
}
TY - JOUR AU - Arapura, Donu TI - Hodge Theory of Cyclic Covers Branchedover a Union of Hyperplanes JO - Canadian journal of mathematics PY - 2014 SP - 505 EP - 524 VL - 66 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-040-8/ DO - 10.4153/CJM-2013-040-8 ID - 10_4153_CJM_2013_040_8 ER -
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