  For certain complex projective manifolds (such as K3 surfaces and their
higher dimensional analogues, the complex symplectic projective manifolds) the
period map takes values in a locally symmetric variety of type IV. It is often
an open embedding and in such cases it has been observed that the image is the
complement of a locally symmetric (Heegner) divisor. We explain that phenomenon
and get our hands on the complementary divisor in terms of geometric data.
