Schottky Problem
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High Quality Content by WIKIPEDIA articles! 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.If one describes the moduli space Ag in intuitive terms, as the parameters on which an abelian variety depends, then the Schottky problem asks simply what condition on the parameters implies that the abelian variety comes from a curve's Jacobian. The classical case, over the complex number field, has received most of the attention, and then an abelian variety…mehr

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High Quality Content by WIKIPEDIA articles! 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.If one describes the moduli space Ag in intuitive terms, as the parameters on which an abelian variety depends, then the Schottky problem asks simply what condition on the parameters implies that the abelian variety comes from a curve's Jacobian. The classical case, over the complex number field, has received most of the attention, and then an abelian variety A is simply a complex torus of a particular type, arising from a lattice in Cg. In relatively concrete terms, it is being asked which lattices are the period lattices of compact Riemann surfaces.