论文标题
整体多型曲曲面的扭转阶层的扭转。
Torsionfreeness for divisor class groups of toric rings of integral polytopes
论文作者
论文摘要
在本文中，我们为$ \ operatoTorname {cl}（\ bbbk [p]）$提供了一些足够条件，为torsionfree，其中$ \ operatatorName {cl}（\ bbbk [p]）$表示triac ring $ \ bbbk $ \ bbbk $ \ bbbk $ f $ p $ p $ p $ p $ p $ p $ p $ p $ p $ p $ p $ p $ p $ p $ p $。 We prove that $\operatorname{Cl}(\Bbbk[P])$ is torsionfree if $P$ is compressed, and $\operatorname{Cl}(\Bbbk[P])$ is torsionfree if $P$ is a $(0,1)$-polytope which has at most $\dim P+2$ facets.此外，我们表征了$（0,1）$ - polytopes $ \ operatatorName {cl}（\ bbbk [p]）\ cong \ mathbb {z} $的曲线环。
In the present paper, we give some sufficient conditions for $\operatorname{Cl}(\Bbbk[P])$ to be torsionfree, where $\operatorname{Cl}(\Bbbk[P])$ denote the divisor class group of the toric ring $\Bbbk[P]$ of an integral polytope $P$. We prove that $\operatorname{Cl}(\Bbbk[P])$ is torsionfree if $P$ is compressed, and $\operatorname{Cl}(\Bbbk[P])$ is torsionfree if $P$ is a $(0,1)$-polytope which has at most $\dim P+2$ facets. Moreover, we characterize the toric rings of $(0,1)$-polytopes in the case $\operatorname{Cl}(\Bbbk[P])\cong \mathbb{Z}$.
