geometry, complex numbers, complex line
$dim = 1$: Riemann surface, super Riemann surface
higher geometry / derived geometry
Ingredients
Concepts
geometric little (∞,1)-toposes
geometric big (∞,1)-toposes
Constructions
Examples
derived smooth geometry
Theorems
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.
For $G$ a complex Lie group then its delooping in complex analytic stack is the moduli stack $\mathbf{B}G$ for holomorphic $G$-principal bundles. For instance for holomorphic vector bundles if $G$ is the general linear group $GL(n,\mathbb{C})$.
Kai Behrend, Behrang Noohi, section 3.2 of Uniformization of Deligne-Mumford curves (arXiv:0504309)
Jacob Lurie, sections 11 and 12 of Closed Immersions
Last revised on July 10, 2020 at 18:13:54. See the history of this page for a list of all contributions to it.