  We describe the application of the results of Kudla-Millson on the modularity
of generating series for cohomology classes of special cycles to the case of
lattice polarized K3 surfaces. In this case, the special cycles can be
interpreted as higher Noether-Lefschetz loci. These generating series can be
paired with the cohomology classes of complete subvarieties of the moduli space
to give classical Siegel modular forms with higher Noether-Lefschetz numbers as
Fourier coefficients. Examples of such complete families associated to
quadratic spaces over totally real number fields are constructed. A more
explicit and concrete construction of such families and the resulting modular
forms would be of interest.
