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2017•Theory and applications of categoriesOpen access

The Canonical 2-Gerbe of a Holomorphic Vector Bundle

Markus Upmeier

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Abstract

For each holomorphic vector bundle we construct a holomorphic bundle 2-gerbe that geometrically represents its second BeilinsonChern 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 KoszulMalgrange type theorem.

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For each holomorphic vector bundle we construct a holomorphic bundle 2-gerbe that geometrically represents its second BeilinsonChern 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 KoszulMalgrange type theorem.

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Available abstract

For each holomorphic vector bundle we construct a holomorphic bundle 2-gerbe that geometrically represents its second BeilinsonChern 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 KoszulMalgrange type theorem.

Key concepts: Cotangent bundle, Holomorphic function, Line bundle, Vector bundle, Normal bundle, Mathematics, Pure mathematics, Identity theorem

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