  We describe a satisfactory theory of degeneration of quadratic forms in three
variables in the most general setting possible: the quadratic forms are defined
on rank 3 vector bundles over an arbitrary scheme and could have values in
nontrivial line bundles. Our results extend what is known for good forms; for
example we show that the Witt-invariant suffices for classification. We
determine explicitly the general, special and usual orthogonal groups and
present applications. We indicate examples of rank 4 vector bundles that do not
admit any Azumaya structures and of rank 3 vector bundles that do not admit any
good quadratic forms with values in specified line bundles. These examples
occur naturally on the Seshadri-desingularisations of moduli spaces of rank two
degree zero vector bundles over a curve relative to an integral normal
locally-Nagata (universally Japanese) base scheme.

Algebraic Geometry;Rings and Algebras