Last syzygies of 1generic 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 1generic 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 1generic if and only if the syzygy varieties Syz(s)=V(I(s)) of all last syzyzgies have the same support as X.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 2003
 arXiv:
 arXiv:math/0307361
 Bibcode:
 2003math......7361B
 Keywords:

 Algebraic Geometry;
 Commutative Algebra;
 13D02;
 14M12
 EPrint:
 AMS Latex, 11 Pages