nLab
complex analytic stack

Contents

Idea

A stack over the site of complex manifolds, hence a 1-truncated complex analytic ∞-stack.

Beware that standard terminology such as for algebraic stack might suggest that a complex analytic stack is a geometric stack over the complex analytic site, but usage as in (Behrend-Noohi 05) differs from that would-be convention.

Examples

For GG a complex Lie group then its delooping in complex analytic stack is the moduli stack BG\mathbf{B}G for holomorphic GG-principal bundles. For instance for holomorphic vector bundles if GG is the general linear group GL(n,)GL(n,\mathbb{C}).

References

Created on July 15, 2014 at 04:56:08. See the history of this page for a list of all contributions to it.