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Catanese surface
In mathematics, a Catanese surface is one of the surfaces of general type introduced by .
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
| 1 | 0 | 0 | 0 | 8 | 0 | 0 | 0 | 1
and canonical degree K^2 = 2. The fundamental group of the Catanese surface is \mathbf{Z}/5\mathbf{Z}, as can be seen from its quotient construction.
References
This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page.
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