Schottky problem [SEP] named after
Schottky problem
In mathematics, the Schottky problem, named after Friedrich Schottky, is a classical question of algebraic geometry, asking for a characterisation of Jacobian varieties amongst abelian varieties.
Geometric formulation.
More precisely, one should consider algebraic curves "C" of a given genus "g", and their Jacobians "J". There is a moduli space "M" of such curves, and a moduli space "A" of abelian varieties of dimension "g", which are "principally polarized".
Prym variety
In mathematics, the Prym variety construction (named for Friedrich Prym) is a method in algebraic geometry of making an abelian variety from a morphism of algebraic curves. In its original form, it was applied to an unramified double covering of a Riemann surface, and was used by F. Schottky and H. W. E. Jung in relation with the Schottky problem, as it is now called, of characterising Jacobian varieties among abelian varieties. It is said to have appeared first in the late work of Riemann, and was