Let X be a \(\mathbb {Q}\)-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; 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 \(\mathrm{Pic}(X)\) in \(\mathrm{Cl}(X)\) is contained in a free part of the latter group.

中文翻译：

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将Picard组嵌入类组中：$$ \ mathbb {Q} $$ Q-阶乘完整复曲面变体的情况

让X是\（\ mathbb {Q} \）上的特性为0的代数闭域-factorial完整复曲面品种有Picard号组的规范注射\（\ mathrm {产品图}（X）\）在Weil除数类的组\（\ mathrm {Cl}（X）\）。这两个群是有限生成的阿贝尔群。第一个是自由团体，而第二个则可能有扭转。我们调查代数和几何条件下，其中所述图像\（\ mathrm {产品图}（X）\）在\（\ mathrm {CL}（X）\）被包含在后一组的自由部分。