互补行列式边理想的Cartwright--Sturmfels性质
Cartwright--Sturmfelsness of complementary determinantal edge ideals
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中文总结 AI 辅助
本文引入互补行列式边理想，完全刻画了使其具有Cartwright--Sturmfels性质的图，并证明该性质等价于存在多元通用Gröbner基，且此类理想为根理想。
中文摘要 AI 辅助
我们引入了互补行列式边理想。对于具有$n$个顶点的图$G$，互补行列式边理想$J_{c}(G)$由通过删除$G$的每条边所索引的两列而得到的通用$(n-2)\ imes n$矩阵的极大子式生成。我们完全刻画了使得$J_{c}(G)$关于按列分次是Cartwright--Sturmfels的图。我们证明该性质等价于存在多元通用Gröbner基，并刻画了满足这些等价条件的图。特别地，满足这些等价条件的理想是根理想。
英文摘要
We introduce complementary determinantal edge ideals. For a graph $G$ on $n$ vertices, the complementary determinantal edge ideal $J_{c}(G)$ is generated by the maximal minors of a generic $(n-2)\times n$ matrix obtained by deleting the two columns indexed by each edge of $G$. We completely characterize the graphs for which $J_{c}(G)$ is Cartwright--Sturmfels with respect to the grading by columns. We prove that this property is equivalent to the existence of a multilinear universal Gröbner basis and characterize the graphs satisfying these equivalent conditions. In particular, the ideals satisfying these equivalent conditions are radical.
发表机构
- Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, The University of Osaka（大阪大学信息理工学研究科应用数学系）
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