Generic Syzygy Schemes
| dc.creator | Bothmer, Hans-Christian Graf v. | |
| dc.date | 2004-03-25 | |
| dc.date.accessioned | 2026-07-07T06:34:23Z | |
| dc.date.available | 2026-07-07T06:34:23Z | |
| dc.description | For 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.description | 12 Pages. This paper is a completely rewritten version of the first part of math.AG/0108078. It also contains several new results | |
| dc.identifier | https://arxiv.org/abs/math/0403432 | |
| dc.identifier | http://arxiv.org/abs/math/0403432 | |
| dc.identifier | Journal of Pure and Applied Algebra, Volume 208, Issue 3 , March 2007, Pages 867-876 | |
| dc.identifier | doi:10.1016/j.jpaa.2006.03.021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99510 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13D02; 14H60 | |
| dc.title | Generic Syzygy Schemes | |
| dc.type | text |