The canonical 2-gerbe of a holomorphic vector bundle

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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.
Original languageEnglish
Pages (from-to)1028-1049
Number of pages23
JournalTheory and Applications of Categories
Volume32
Issue number30
Publication statusPublished - 2017

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