Szego kernels and finite group actions

In the context of almost complex quantization, a natural generalization of algebro-geometric linear series on a compact symplectic manifold has been proposed. Here we suppose given a compatible action of a finite group and consider the linear subseries associated to the irreducible representations of G, give conditions under which these are base-point-free and study properties of the associated projective morphisms. The results obtained are new even in the complex projective case.