nLab holomorphic line n-bundle

Idea

The concept of line n-bundle in complex analytic geometry, classified by maps into the $n$-fold delooping $\mathbf{B}^n \mathbb{G}_m$ of the multiplicative group.

• for $n = 0$ these are holomorphic functions classified by the group of units;

• for $n= 1$ these are holomorphic line bundles, classified by Picard group, modulated by Picard stack;

• for $n =2$ these are holomorphic line 2-bundles, classified by Brauer group, modulated by Brauer stack

Properties

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Related concepts

• algebraic line n-bundle

• complex analytic ∞-stack

References

• Alexander Grothendieck, Le groupe de Brauer : II. Théories cohomologiques. Séminaire Bourbaki, 9 (1964-1966), Exp. No. 297, 21 p. (Numdam)