Manifolds and cobordisms
A complex manifold is a manifold holomorphically modeled on polydiscs in (complexified -dimensional cartesian space):
Every complex manifold admits a good open cover in .
For instance (Maddock, lemma 3.2.8).
Complex 1-dimensional: Riemann surfaces
A complex manifold of complex dimension 1 is called a Riemann surface.
A complex manifold whose canonical bundle is trivializable is a Calabi-Yau manifold. In complex dimension 2 this is a K3 surface.
Textbook accounts include
Lectures notes inclide
Stefan Vandoren, Lectures on Riemannian Geometry, Part II: Complex Manifolds (pdf)
Zachary Maddock, Dobeault cohomology (pdf)
Revised on July 17, 2014 14:19:58
by Todd Trimble