Maximal variation of linear systems

Abstract

Let X be a smooth projective complex variety, and L a line bundle on X . We say that the linear system |L| has maximal variation if its elements have the maximum number dim|L| of moduli. We discuss some cases where this situation is expected: hypersurfaces, double coverings of the projective space, K3 surfaces, hyperkähler manifolds, and abelian varieties.

Final version, to appear in Selecta Mathematica