Determinantal hypersurfaces
| dc.creator | Beauville, A. | |
| dc.date | 1999-10-06 | |
| dc.date | 2000-05-02 | |
| dc.date.accessioned | 2026-07-07T05:31:04Z | |
| dc.date.available | 2026-07-07T05:31:04Z | |
| dc.description | Let X be a smooth hypersurface in projective space. We discuss in this paper when X can be defined by an equation det M = 0 (resp. pf M = 0), where M is a matrix (resp. a skew-symmetric matrix) with homogeneous entries. Standard homological algebra methods show that this is equivalent to produce a line bundle (resp. a rank 2 vector bundle) E of a certain type on X . We discuss a number of applications for hypersurfaces of small dimension. An Appendix by F.-O. Schreyer proves (using Macaulay 2) that a general form of degree d in P^3 (resp. P^4) can be written as the pfaffian of a skew-symmetric (2d)x(2d) matrix with linear entries in the expected range, that is d < 16 (resp. d < 6). | |
| dc.description | 29 pages, Plain TeX, with a new Appendix by F.-O. Schreyer | |
| dc.identifier | https://arxiv.org/abs/math/9910030 | |
| dc.identifier | http://arxiv.org/abs/math/9910030 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79208 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Determinantal hypersurfaces | |
| dc.type | text |