Abelian surface: Difference between revisions

Revision as of 20:53, 19 February 2007

In algebraic geometry an Abelian surface over a field $K$ is a two dimensional Abelian variety. Every abelian surface is either a Jacobian variety of a smooth hyperelliptic curve of genus two, or a product of two elliptic curves. Abelian surfaces are one of the two types of algebraic surfaces with trivial canonical class, the other type being algebraic K3 surfaces.

Below we consider the case where an Abelian variety is the Jacobian of a curve $H$ of genus 2.

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 In [[algebraic geometry]] an Abelian surface over a [[field]] <math>K</math> is a two dimensional [[Abelian variety]]. Every abelian surface is either a [[Jacobian variety]] of a smooth [[hyperelliptic curve]] of [[genus]] two, or a product of two [[elliptic curves]]. Abelian surfaces are one of the two types of [[algebraic surfaces]] with trivial [[canonical class]], the other type being algebraic [[K3 surfaces]].
+== The Kummer surface ==
+=== the quadric line complex ===
+=== Kummer's quartic surface ===
+=== the <math>16_6</math> configurations ===
+== polarization ==
+== Jacobians of curves of genus 2 ==
+Below we consider the case where an Abelian variety is the Jacobian of a curve <math>H</math> of genus 2.
+=== addition algorithm ===
+[[Category:Mathematics Workgroup]]
+[[Category:CZ Live]]