nLab
moduli space of complex structures

Contents

Contents

Idea

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 Teichm├╝ller 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.

moduli spaces

References

The moduli space of complex structures on a manifold is discussed for instance from page 175 on of

  • Yongbin Ruan, Symplectic topology and complex surfaces in Geometry and analysis on complex manifolds (1994)

and in

  • Yurii M. Burman, Relative moduli spaces of complex structures: an example (arXiv:math/9903029)

Last revised on October 14, 2019 at 12:47:08. See the history of this page for a list of all contributions to it.