DMS Algebra Seminar

Speaker: Cheng Meng (Purdue)

Title: Decompositions of local cohomology tables

Abstract: Let R be a standard graded polynomial ring over a field k, then the Boij-S\"oderberg theory describes the cone spanned by the Betti tables of finitely generated graded R-modules. This theory shows that the extremal rays of the cone are given by the pure Betti tables and every Betti table is a finite linear combination of pure Betti tables with positive rational coefficients. In this talk, we will focus on the cone spanned by the local cohomology tables of finitely generated graded R-modules of projective dimension at most 1. We will describe the extremal rays of the cone generated by local cohomology tables of such modules and show that not every local cohomology table of such a module is a finite linear combination of the tables on the extremal ray with positive rational coefficients.