nLab Prym variety

Idea

In good cases a homomorphism $f\colon C_1 \to C_2$ of algebraic curves allows to push-forward algebraic line bundles such as to induce a homomorphism of the corresponding Jacobian varieties/Picard varieties $J_1 \to J_2$. The Prym variety of $f$ then is the kernel of this map, hence the space of algebraic line bundles on $C_1$ which pushes to the trivial line under $f$.

Related concepts

• Prym-Tyurin variety

References

• Wikipedia, Prym variety