Monday 16 February 2026
11:00–12:30*

Junyan Chu (Kyoto University) — Arrangements Close to Free: Two Deletions, Resolutions, and a Saito-Type Relation

Abe showed that deleting one hyperplane from a free arrangement yields an arrangement that is either free or SPOG. We study arrangements obtained by deleting two hyperplanes from a free arrangement, which typically destroys freeness. Using minimal free resolutions of logarithmic derivation modules, we prove lower bounds on graded Betti numbers and, in dimension three, explicitly compute these resolutions and provide examples. Finally, when the derivation module has projective dimension at most one, we prove a Saito-like relation among minimal generators. This implies that the arrangement is SPOG and suggests a broader generalization of Saito's criterion beyond the free case.

* Eastern European Time, i.e. UTC+2 in winter and UTC+3 in summer.