The Canonical 2-Gerbe of a Holomorphic Vector Bundle
Differential Geometry
2017-09-15 v2
Abstract
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.
Cite
@article{arxiv.1601.04819,
title = {The Canonical 2-Gerbe of a Holomorphic Vector Bundle},
author = {Markus Upmeier},
journal= {arXiv preprint arXiv:1601.04819},
year = {2017}
}
Comments
Revised version. 18 pages