  The isometry class of the intersection form of a compact complex surface can
be easily determined from complex-analytic invariants. For projective surfaces
the primitive lattice is another naturally occurring lattice. The goal of this
note is to show that it can be determined from the intersection lattice and the
self-intersection of a primitive ample class, at least when the primitive
lattice is indefinite. Examples include the Godeaux surfaces, the Kunev surface
and a specific Horikawa surface. There are also some results concerning
(negative) definite primitive lattices, especially for canonically polarized
surfaces of general type.
