David R. Kohel
Institut de Mathematiques de Luminy
Lower dimensional CM constructions

Algorithms for constructive complex multiplication of elliptic curves 
have seen research on various fronts, including:  
  1. Choice of a moduli space X, with low degree cover X -> Y having a 
     rational parametrization P^1 -> Y.
  2. Complex analytic, p-adic, and CRT algorithms for determining CM points. 
  3. Galois theoretic properties of these points based on geometric and 
     class field theoretic considerations.
  4. Construction of class polynomials, or ideals, over Q from CM points.
We will discuss generalizations of these questions to Jacobian surfaces 
other low dimensional abelian varieties.