In mathematics, a Catanese surface is one of the surfaces of general type introduced by Catanese (1981).
Contents
Construction
The construction starts with a quintic V with 20 double points. Let W be the surface obtained by blowing up the 20 double points. Suppose that W has a double cover X branched over the 20 exceptional −2-curves. Let Y be obtained from X by blowing down the 20 −1-curves in X. If there is a group of order 5 acting freely on all these surfaces, then the quotient Z of Y by this group of order 5 is a Catanese surface. Catanese found a 4-dimensional family of curves constructed like this.
Invariants
The fundamental group is trivial. The irregularity and the geometric genus are both 0.
References
Catanese surface Wikipedia(Text) CC BY-SA