nLab complex surface

Idea

A complex surface is a surface in complex analytic geometry, hence a complex analytic space of complex dimension 2 (hence of real dimension 4).

Examples

• K3 surface

Related concepts

• algebraic surface

• complex manifold, almost complex manifold

  complex surface, complex curve

  Kähler manifold, hyper-Kähler manifold

  Calabi-Yau manifold

References

• Robert Friedman, John Morgan, Smooth Four-Manifolds and Complex Surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (1994) (doi:10.1007/978-3-662-03028-8)

See also

• Wikipedia, Complex surfaces

Discussion of patterns in the characteristic classes (Chern classes) of complex surfaces, together with some speculations about an anlogy with atomic number of atomic nuclei is in

• Michael Atiyah, Nicholas Manton, Complex Geometry of Nuclei and Atoms (arXiv:1609.02816)