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.
Rossi, M., Terracini, L. (2021). Embedding the Picard group inside the class group: the case of Q -factorial complete toric varieties. JOURNAL OF ALGEBRAIC COMBINATORICS, 53(2), 553-573 [10.1007/s10801-021-01025-x].
Embedding the Picard group inside the class group: the case of Q -factorial complete toric varieties
Rossi M.;
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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