Embedding the Picard group inside the class group: the case of $\Q$-factorial complete toric varieties

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 $\mathrm{Pic}(X)$ in the group $\mathrm{Cl}(X)$ of classes of Weil divisors. These two groups are finitely generated abelian groups; whilst the first one is a free group, the second one may have torsion. We investigate algebraic and geometrical conditions under which the image of $\mathrm{Pic}(X)$ in $\mathrm{Cl}(X)$ is contained in a free part of the latter group.

18 pages - References updated

References in corpus (2)

• Z-linear Gale duality and poly weighted spaces (PWS)
• A Q-factorial complete toric variety is a quotient of a poly weighted space

Cited by in corpus (1)

• Étale coverings in codimension 1 with applications to Mori Dream Spaces