Affiliation:
1. Dipartimento di Matematica, Università di Genova , Via Dodecaneso 35, 16146 Genova, Italy
Abstract
Abstract
Closed graphs have been characterized by Herzog et al. as the graphs whose binomial edge ideals have a quadratic Gröbner basis with respect to a diagonal term order. In this paper, we focus on a generalization of closed graphs, namely weakly closed graphs (or co-comparability graphs). Building on some results about Knutson ideals of generic matrices, we characterize weakly closed graphs as the only graphs whose binomial edge ideals are Knutson ideals for a certain polynomial $f$. In doing so, we re-prove Matsuda’s theorem about the F-purity of binomial edge ideals of weakly closed graphs in positive characteristic and we extend it to generalized binomial edge ideals. Furthermore, we give a characterization of weakly closed graphs in terms of the minimal primes of their binomial edge ideals and we characterize all minimal primes of Knutson ideals for this choice of $f$.
Publisher
Oxford University Press (OUP)
Cited by
2 articles.
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1. The v-Number of Binomial Edge Ideals;Acta Mathematica Vietnamica;2024-07-04
2. Singularities of determinantal pure pairs;Bollettino dell'Unione Matematica Italiana;2023-05-05