  For each holomorphic vector bundle we construct a holomorphic bundle 2-gerbe
that geometrically represents its second Beilinson-Chern class. Applied to the
cotangent bundle, this may be regarded as a higher analogue of the canonical
line bundle in complex geometry. Moreover, we exhibit the precise relationship
between holomorphic and smooth gerbes. For example, we introduce an Atiyah
class for gerbes and prove a Koszul-Malgrange type theorem.

Differential Geometry