Period Lattice Formulation
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.
Read more about this topic: Schottky Problem
Famous quotes containing the words period and/or formulation:
“The easiest period in a crisis situation is actually the battle itself. The most difficult is the period of indecision—whether to fight or run away. And the most dangerous period is the aftermath. It is then, with all his resources spent and his guard down, that an individual must watch out for dulled reactions and faulty judgment.”
—Richard M. Nixon (1913–1995)
“Art is an experience, not the formulation of a problem.”
—Lindsay Anderson (b. 1923)