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arXiv · 2610.07812

Cartwright--Sturmfelsness of complementary determinantal edge ideals

Koichiro Tani
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Abstract

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.

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Koichiro Tani. 2026-10-06. Cartwright--Sturmfelsness of complementary determinantal edge ideals. https://arxiv.org/abs/2610.07812

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