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 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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- July 2003
- DOI:
- 10.48550/arXiv.math/0307361
- arXiv:
- arXiv:math/0307361
- Bibcode:
- 2003math......7361B
- Keywords:
-
- Algebraic Geometry;
- Commutative Algebra;
- 13D02;
- 14M12
- E-Print:
- AMS Latex, 11 Pages