整多面体环面环的除子类群的无挠性
Torsionfreeness for divisor class groups of toric rings of integral polytopes
摘要：
本文给出了$\operatorname{Cl}(\Bbbk[P])$无挠的几个充分条件，其中$\operatorname{Cl}(\Bbbk[P])$表示整多胞形$P$的复曲面环$\Bbbk[P]$的除子类群.证明了当$P$压缩时，$\operatorname{Cl}(\Bbbk[P])$是无挠的;当$P$是至多有$\dim P+2$小平面的$(0,1)$ -多面体时，$\operatorname{Cl}(\Bbbk[P])$是无挠的.此外，我们还刻画了$\operatorname{Cl}(\Bbbk[P])\cong \mathbb{Z}$情形下$(0,1)$ -多面体的环面环。
英文摘要：
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 $\operatorname{Cl}(\Bbbk[P])\cong \mathbb{Z}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
