Cartwright--Sturmfelsness of complementary determinantal edge ideals

@misc{tani2026cartwrightsturmfelsness,
  title = {{Cartwright--Sturmfelsness of complementary determinantal edge ideals}},
  author = {Koichiro Tani},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.07812},
  eprint = {2610.07812},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.07812},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Cartwright--Sturmfelsness of complementary determinantal edge ideals
AU  - Koichiro Tani
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.07812
UR  - https://arxiv.org/abs/2610.07812
AB  - 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)× 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.
ER  -