Godeaux surface [SEP] named after
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 (such as Barlow surfaces) are called numerical Godeaux surfaces.
Construction.
The cyclic group of order 5 acts freely on the Fermat surface of points ("w : x : y : z")
in "
the original Godeaux surface. Other surfaces constructed in a similar way with the same Hodge numbers are also sometimes called Godeaux surfaces. Surfaces with the same Hodge numbers (such as Barlow surfaces) are called numerical Godeaux surfaces. The fundamental group (of the original Godeaux surface) is cyclic of order 5.
- "c" = 11: Barlow surfaces are simply connected, and are the only known examples of simply connected surfaces of general type with "p" = 0.
- Todorov surfaces give