Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Tani, Koichiro
Institution: The University of Osaka
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221041188