A complex surface is a complex manifold of complex dimension two, meaning that its coordinate
charts take values in open subsets of 
. Its underlying real manifold
has dimension four. Important examples include K3
surfaces and two-dimensional complex tori.
Complex Surface
See also
Algebraic Surface, Bloch Conjecture, Class VII Surface, Complex Manifold, Complex Torus, Global Spherical Shell, Global Spherical Shell Conjecture, K3 Surface, Oka ManifoldExplore with Wolfram|Alpha
References
Barth, W. P.; Peters, C. A. M.; and van de Ven, A. A. Compact Complex Surfaces. New York: Springer-Verlag, 1984.Cite this as:
Weisstein, Eric W. "Complex Surface." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ComplexSurface.html