Last syzygies of 1-generic spaces
Abstract
Consider a determinantal variety X of expected codimension definend by the maximal minors of a matrix M of linear forms. Eisenbud and Popescu have conjectured that 1-generic matrices M are characterised by the property that the syzygy ideals I(s) of all last syzygies s of X coincide with IX. In this note we prove a geometric version of this characterization, i.e. that M is 1-generic if and only if the syzygy varieties Syz(s)=V(I(s)) of all last syzyzgies have the same support as X.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.