nLab complex geometry - contents

geometry, complex numbers, complex line

complex geometry

• complex manifold, complex structure

• complex analytic space

Variants

• generalized complex geometry

• complex supermanifold

Structures

• Dolbeault complex, holomorphic de Rham complex

• Hodge structure, Hodge filtration

• Hodge-filtered differential cohomology

Examples

• $dim = 1$: Riemann surface, super Riemann surface

• Calabi-Yau manifold

  • $dim = 2$: K3 surface

• generalized Calabi-Yau manifold