Generic Syzygy Schemes

dc.creatorBothmer, Hans-Christian Graf v.
dc.date2004-03-25
dc.date.accessioned2026-07-07T06:34:23Z
dc.date.available2026-07-07T06:34:23Z
dc.descriptionFor a finite dimensional vector space G we define the k-th generic syzygy scheme Gensyz_k(G) by explicit equations. We show that the syzygy scheme Syz(f) of any syzygy in the linear strand of a projective variety X which is cut out by quadrics is a cone over a linear section of a corresponding generic syzygy scheme. We also give a geometric description of Gensyz_k(G) for k=0,1,2. In particular Gensyz_2(G) is the union of a Pl"ucker embedded Grassmannian and a linear space. From this we deduce that every smooth, non-degenerate projective curve C which is cut out by quadrics and has a p-th linear syzygy of rank p+3 admits a rank 2 vector bundle E with det E = O_C(1) and h^0(E) at least p+4.
dc.description12 Pages. This paper is a completely rewritten version of the first part of math.AG/0108078. It also contains several new results
dc.identifierhttps://arxiv.org/abs/math/0403432
dc.identifierhttp://arxiv.org/abs/math/0403432
dc.identifierJournal of Pure and Applied Algebra, Volume 208, Issue 3 , March 2007, Pages 867-876
dc.identifierdoi:10.1016/j.jpaa.2006.03.021
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99510
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subject13D02; 14H60
dc.titleGeneric Syzygy Schemes
dc.typetext

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