Last syzygies of 1-generic spaces
arXiv:math/0307361 · doi:10.1016/j.jalgebra.2004.02.032
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 I_X. 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.
AMS Latex, 11 Pages