Pfaffian Subschemes
| dc.creator | Walter, Charles H. | |
| dc.date | 1994-06-17 | |
| dc.date.accessioned | 2026-07-07T09:06:06Z | |
| dc.date.available | 2026-07-07T09:06:06Z | |
| dc.description | A subscheme $X\subset \Bbb P^{n+3}$ of codimension $3$ is {\em Pfaffian} if it is the degeneracy locus of a skew-symmetric map $f:\cal{E}\spcheck(-t) @>>> \cal{E}$ with $\cal{E}$ a locally free sheaf of odd rank on $\Bbb P^{n+3}$. It is shown that a codimension $3$ subscheme $X\subset\Bbb P^{n+3}$ is Pfaffian if and only if it is locally Gorenstein, subcanonical (i.e.\ $ω_X\cong\cal O_X(l)$ for some integer $l$), and the following parity condition holds: if $n\equiv 0\pmod{4}$ and $l$ is even, then $χ(\cal O_X (l/2))$ is also even. The paper includes a modern version of the Horrocks correspondence, stated in the language of derived categories. A local analogue of the main theorem is also proved. | |
| dc.description | 26 pages, AMS-LaTeX | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9406005 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9406005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149900 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Pfaffian Subschemes | |
| dc.type | text |