  We consider a moduli space of lattice polarized K3 surfaces with the
additional information of a frame of the trascendental cohomology with respect
to the lattice polarization. This moduli space is proved to be quasi-affine,
and the existence of vector fields on it, called modular vector fields, is
proved. A purely algebraic version of the algebra of Siegel quasi-modular forms
is obtained as the algebra of global regular functions over this moduli space,
with a differential structure coming from the modular vector fields. By means
of trascendental considerations we are able to obtain a differential algebra of
meromorphic Siegel quasi-modular forms from the previous algebra.
