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 $ψ$

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

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 $ψ$