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.
Keywords: Holomorphic Gerbes, Second Chern class, Complex manifolds, Holomorphic vector bundles
2010 MSC: 18F15
Theory and Applications of Categories, Vol. 32, 2017, No. 30, pp 1028-1049.