Schur quadrics, cubic surfaces and rank 2 vector bundles over the projective plane
| dc.creator | Dolgachev, I. | |
| dc.creator | Kapranov, M. | |
| dc.date | 1993-04-13 | |
| dc.date.accessioned | 2026-07-07T09:05:49Z | |
| dc.date.available | 2026-07-07T09:05:49Z | |
| dc.description | A cubic surface in $P^3$ is known to contain 27 lines, out of which one can form 36 Schlafli double - sixes i.e., collections $l_1,...,l_6, l'_1,..., l'_6\}$ of 12 lines such that each $l_i$ meets only $l'_j, j\neq i$ and does not meet $l_j, j\neq i$. In 1881 F. Schur proved that any double - six gives rise to a certain quadric $Q$ , called Schur quadric which is characterized as follows: for any $i$ the lines $l_i$ and $l'_i$ are orthogonal with respect to (the quadratic form defining) $Q$. The aim of the paper is to relate Schur's construction to the theory of vector bundles on $P^2$ and to generalize this construction along the lines of the said theory. | |
| dc.description | 27 pages, plain TEX | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9304005 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9304005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149805 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Schur quadrics, cubic surfaces and rank 2 vector bundles over the projective plane | |
| dc.type | text |