Last syzygies of 1-generic spaces

Details Last syzygies of 1-generic spaces Last syzygies of 1-generic spaces

2003-07-28

arxiv.org/abs/math/0307361v1

Journal of Algebra, Volume 278, Issue 1, 2004, pp 360-369

Mathematics

Algebraic Geometry

AMS Latex, 11 Pages

Scientific paper

10.1016/j.jalgebra.2004.02.032

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.

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