30 April 2025 — Padova

ADE correspondence for finite free resolutions

Jerzy Weyman, Jagiellonian University

Abstract

I will discuss recent results joint with Lorenzo Guerrieri and Xianglong Ni on finite free resolutions over local rings. The main result is the classification of perfect ideals of codimension \(3\) in the linkage class of a complete intersection (licci ideals). The proofs are based on a connection of the problem to root systems of type \(T_{p,q,r}\). In particular one proves that if \(T_{p,q,r}\) is a graph of type ADE then every perfect ideal with the resolution of corresponding format is licci.