Английская Википедия:Catanese surface
In mathematics, a Catanese surface is one of the surfaces of general type introduced by Шаблон:Harvs.
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 Catanese surface is a numerical Campedelli surface and hence has Hodge diamond
and canonical degree <math>K^2 = 2</math>. The fundamental group of the Catanese surface is <math>\mathbf{Z}/5\mathbf{Z}</math>, as can be seen from its quotient construction.
References
