  We give examples of subcanonical subvarieties of codimension 3 in projective
n-space which are not Pfaffian, i.e. defined by the ideal sheaf of submaximal
Pfaffians of an alternating map of vector bundles. This gives a negative answer
to a question asked by Okonek.
  Walter had previously shown that a very large majority of subcanonical
subschemes of codimension 3 in P^n are Pfaffian, but he left open the question
whether the exceptional non-Pfaffian cases actually occur. We give non-Pfaffian
examples of the principal types allowed by his theorem, including (Enriques)
surfaces in P^5 in characteristic 2 and a smooth 4-fold in P^7.
  These examples are based on our previous work math.AG/9906170 showing that
any strongly subcanonical subscheme of codimension 3 of a Noetherian scheme can
be realized as a locus of degenerate intersection of a pair of Lagrangian
(maximal isotropic) subbundles of a twisted orthogonal bundle.
