In mathematics, a Catanese surface is one of the surfaces of general type introduced by Catanese (1981).
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.
The Catanese surface is a numerical Campedelli surface and hence has Hodge diamond
In mathematics, a Campedelli surface is one of the surfaces of general type introduced by Campedelli. Surfaces with the same Hodge numbers are called numerical Campedelli surfaces.
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and canonical degree . The fundamental group of the Catanese surface is , as can be seen from its quotient construction.
In mathematics, an elliptic curve is a plane algebraic curve defined by an equation of the form
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This is a glossary of algebraic geometry.
The International Standard Book Number (ISBN) is a numeric commercial book identifier which is intended to be unique. Publishers purchase ISBNs from an affiliate of the International ISBN Agency.
Mathematical Reviews is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also publishes an associated online bibliographic database called MathSciNet which contains an electronic version of Mathematical Reviews and additionally contains citation information for over 3.5 million items as of 2018.
