In mathematics, the Prym variety construction is a method in algebraic geometry of making an abelian variety from a morphism of algebraic curves
In mathematics, the Prym variety construction is a method in algebraic geometry of making an abelian variety from a morphism of algebraic curves
Given a non-constant morphism
$$ φ: C_1 → C_2$$
of algebraic curves, write $J_i$ for the Jacobian variety of $C_i$. Then from $φ$ construct the corresponding morphism
$$ψ: J_1 → J_2,$$
which can be defined on a divisor class $D$ of degree zero by applying $φ$ to each point of the divisor. This is a well-defined morphism, often called the norm homomorphism. Then the Prym variety of $φ$ is the kernel of $ψ$
See also:
- Wikipedia article Prym variety
- Prim variety in nLab
