Godeaux surface
In mathematics, a Godeaux surface is one of the surfaces of general type introduced by Lucien Godeaux in 1931.
Other surfaces constructed in a similar way with the same Hodge numbers are also sometimes called Godeaux surfaces. Surfaces with the same Hodge numbers are called numerical Godeaux surfaces.Construction
The cyclic group of order 5 acts freely on the Fermat surface of points
in P3 satisfying w5 + x5 + y5 + z5 = 0 by mapping to where ρ is a fifth root of 1. The quotient by this action is the original Godeaux surface.Invariants
The fundamental group is cyclic of order 5.
It has invariants like rational surfaces do, though it is not rational. The square of the first Chern class .
