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

VL - 32

SP - 1028

EP - 1049

JO - Theory and Applications of Categories

JF - Theory and Applications of Categories

SN - 1201-561X

IS - 30

ER -