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

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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https://link.springer.com/article/10.1007/s10801-021-01025-x
Cartier and Weil divisors; Completion of fans; Free and torsion subgroups; Localization; Pure modules; Q-factorial complete toric varieties
Rossi M.; Terracini L.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1783216
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