On symmetric degeneracy loci, spaces of symmetric matrices of constant rank and dual varieties
| dc.creator | Ilic, Bo | |
| dc.creator | Landsberg, J. M. | |
| dc.date | 1996-11-20 | |
| dc.date.accessioned | 2026-07-07T09:07:05Z | |
| dc.date.available | 2026-07-07T09:07:05Z | |
| dc.description | Let X be a nonsingular simply connected projective variety of dimension m, E a rank n vector bundle on X, and L a line bundle on X. Suppose that $S^2(E^{*}) \otimes L$ is an ample vector bundle and that there is a constant even rank $r \ge 2$ symmetric bundle map $E \to E^{*} \otimes L$. We prove that $m \le n-r$. We use this result to solve the constant rank problem for symmetric matrices, proving that the maximal dimension of a linear subspace of the space of $m\times m$ symmetric matrices such that each nonzero element has even rank $r \ge 2$ is $m-r+1$. We explain how this result relates to the study of dual varieties in projective geometry and give some applications and examples. | |
| dc.description | AMS-TeX, 15 pages | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9611025 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9611025 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150243 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.title | On symmetric degeneracy loci, spaces of symmetric matrices of constant rank and dual varieties | |
| dc.type | text |