  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.\ $\omega_X\cong\cal
O_X(l)$ for some integer $l$), and the following parity condition holds: if
$n\equiv 0\pmod{4}$ and $l$ is even, then $\chi (\cal O_X (l/2))$ 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.

Algebraic Geometry;Algebraic Geometry