  For arbitrary quantizable compact Kaehler manifolds, relations between the
geometry given by the coherent states based on the manifold and the algebraic
(projective) geometry realised via the coherent state mapping into projective
space, are studied. Polar divisors, formulas relating the scalar products of
coherent vectors on the manifold with the corresponding scalar products on
projective space (Cauchy formulas), two-point, three-point and more generally
cyclic m-point functions are discussed. The three-point function is related to
the shape invariant of geodesic triangles in projective space.
