Virtual Commutative algebra seminar
Date and Time: Friday, 13 January 2023, 5:30 pm
Gmeet link: https://meet.google.com/ekz-uhiv-grs
Host: J. K. Verma
Speaker: Lisa Seccia
Affiliation: University of Genoa, Genoa, Italy
Title: Weakly-closed graphs and F-purity of binomial edge ideals
Abstract: Herzog et al. characterized closed graphs as the graphs whose binomial edge ideals have a quadratic Groebner basis. In this talk, we focus on a generalization of closed graphs, namely weakly-closed graphs (or co-comparability graphs). Building on known results about Knutson ideals of generic matrices, we characterize weakly-closed graphs as the only graphs whose binomial edge ideals are Knutson ideals (associated with 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 prime characteristic and we extend it to generalized binomial edge ideals.
Lastly, we will discuss some open conjectures on the F-purity of binomial edge ideals and on the relation between Knutson ideals and compatible ideals.