Last syzygies of 1-generic spaces

2003/07/28 by Hans‐Christian Graf von Bothmer, Hans-Christian v. Bothmer
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #math.AC #math.AG #msc:13D02 #msc:14M12

paper · pdf · doi:10.1016/j.jalgebra.2004.02.032

published as Journal of Algebra, Volume 278, Issue 1, 2004, pp 360-369 · AMS Latex, 11 Pages

arxiv created 2003/07/28 · openalex publication_date 2004/05/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• green's canonical syzygy conjecture for generic curves of odd genus

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