Seminario del prof. Jerzy Weyman - 15 aprile 2026.

Mercoledì il 15 Aprile alle ore 15,30 in aula 22 il Prof. Jerzy Weyman (Jagiellonian University - Krakow) terrà un seminario dal titolo: Finite free resolutions: beyond Hilbert-Burch and Buchsbaum-Eisenbud.

Abstract: I will describe a joint project with Tymoteusz Chmiel, Lorenzo Guerrieri and Xianglong N ion finite free resolutions. It is well known that for perfect ideals of codimension 2 in a local ring, and for Gorenstein ideals there are generic models (n x n minrs of an n x (n+1) matrix (Hilbert-Burch model) and submaximal Pfaffians of (2n+1) x (2n+1) skew-symmetric matrix (Buchsbaum-Eisenbud model). Our project involves identifying other formats for which such generic models exist for perfect ideals of codimension 3 and Gorenstein ideals of codimension 4. There are very few such formats (for Gorenstein ideals of codimension 4 these are ideals generated by up to 8 generators. The whole idea is linked to the  Cartan-Killing classification of simple Lie algebras and to the ADE classification of simply laced root systems.

Hilbert-Burch models correspond to type A, Buchsbaum-Eisenbud models to type D, and the remaining new models correspond to types E_6, E_7, E_8. Another application is to the classification of the perfect ideals in the linkage class of a complete intersection (so-called Herzog class). We can do it for perfect ideals of codimension 3, for Gorenstein ideals of codimension 4. Conjecturally this result should extend to arbitrary codimension.