KTH/SU Mathematics Colloquium
07-04-11
Gerard van der Geer, University of Amsterdam
The Schottky Problem
An algebraic curve determines an abelian variety, the Jacobian
of the curve. For example, for a Riemann surface the Jacobian is
a complex torus associated to the periods of integrals over the
Riemann surface. Not every abelian variety is the Jacobian of a
curve and the Schottky problem, due to Riemann, asks for a characterization
of the Jacobians among all abelian varieties. Various answers have been
proposed. We shall discuss the problem, its history and some of the
proposed answers to this problem.