环面簇的自同构与Gale对偶
Automorphisms of toric varieties and Gale duality
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中文总结 AI 辅助
本文利用Gale对偶分类了满足自同构群具有开轨道且补集无除子的完备环面三维簇，并确定了自同构群在光滑点集上可递的簇。
中文摘要 AI 辅助
我们分类了完备环面三维簇$X$，使得自同构群$\text{Aut}(X)$在$X$上作用时具有一个开轨道，且该轨道的补集不包含除子。后一条件意味着对于扇$\Sigma_X$的任意射线$\rho$，存在与$\rho$相关联的$\Sigma_X$的Demazure根。我们还在这些簇中找出那些$\text{Aut}(X)$在光滑点集$X^{\text{reg}}$上可递的$X$。这些分类基于这些性质的Gale对偶解释。
英文摘要
We classify complete toric threefolds $X$ such that the automorphism group $\text{Aut}(X)$ acts on $X$ with an open orbit whose complement does not contain a divisor. The latter condition means that for any ray $ρ$ of the fan $Σ_X$ there is a Demazure root of $Σ_X$ associated with $ρ$. We also find among these varieties those $X$ for which the group $\text{Aut}(X)$ is transitive on the smooth locus $X^{\text{reg}}$. The classifications are based on Gale-dual interpretations of these properties.
发表机构
- HSE University（高等经济大学）
机构由 AI 辅助整理，请以论文原文为准。
