TY - JOUR
T1 - The canonical 2-gerbe of a holomorphic vector bundle
AU - Upmeier, Markus
N1 - I thank Joel Fine for many discussions on these results.
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
UR - http://www.tac.mta.ca/tac/volumes/32/30/32-30.pdf
UR - https://arxiv.org/pdf/1601.04819.pdf
M3 - Article
SN - 1201-561X
VL - 32
SP - 1028
EP - 1049
JO - Theory and Applications of Categories
JF - Theory and Applications of Categories
IS - 30
ER -