Let X be a Q-factorial complete toric variety over an algebraic closed field of characteristic 0. There is a canonical injection of the Picard group Pic (X) in the group Cl (X) of classes of Weil divisors. These two groups are finitely generated abelian groups; while the first one is a free group, the second one may have torsion. We investigate algebraic and geometrical conditions under which the image of Pic (X) in Cl (X) is contained in a free part of the latter group.
Embedding the Picard group inside the class group: the case of Q -factorial complete toric varieties
Rossi M.;Terracini L.
2021-01-01
Abstract
Let X be a Q-factorial complete toric variety over an algebraic closed field of characteristic 0. There is a canonical injection of the Picard group Pic (X) in the group Cl (X) of classes of Weil divisors. These two groups are finitely generated abelian groups; while the first one is a free group, the second one may have torsion. We investigate algebraic and geometrical conditions under which the image of Pic (X) in Cl (X) is contained in a free part of the latter group.
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