geometry, complex numbers, complex line
$dim = 1$: Riemann surface, super Riemann surface
A moduli space/moduli stack of complex structures on a given topological manifold/smooth manifold.
For complex structures on 2-dimensional manifolds the moduli space of complex structures modulo homeomorphisms isotopic to the identity is Teichmüller space, and the further orbifold quotient of that by the mapping class group is an orbifold/Deligne-Mumford stack called the Riemann moduli stack of complex curves.
Specifically for once-punctured 2-dimensional manifolds of genus 1 (tori) this is equivalently the moduli stack of elliptic curves over the complex numbers.
The moduli space of complex structures on a manifold is discussed for instance from page 175 on of
and in
Last revised on October 14, 2019 at 12:47:08. See the history of this page for a list of all contributions to it.