Given a normal complete variety Y, distinct irreducible effective Weil divisors D1,...Dn of Y and positive integers d1,...dn, we spell out the conditions for the existence of an abelian cover X → Y branched with order di on Di for i = 1,...n. As an application, we prove that a Galois cover of a normal complete toric variety branched on the torus-invariant divisors is itself a toric variety.
On the existence of ramified abelian covers
PARDINI, RITA
2013-01-01
Abstract
Given a normal complete variety Y, distinct irreducible effective Weil divisors D1,...Dn of Y and positive integers d1,...dn, we spell out the conditions for the existence of an abelian cover X → Y branched with order di on Di for i = 1,...n. As an application, we prove that a Galois cover of a normal complete toric variety branched on the torus-invariant divisors is itself a toric variety.File in questo prodotto:
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