Degree of the divisor of solutions of a differential equation on a projective variety

Using the data schemes from [I] we give a rigorous definition of algebraic differential equations on the complex projective space P-n. For an algebraic subvariety S subset of or equal to P-n, we present an explicit formula for the degree of the divisor of solutions of a differential equation on S and give some examples of applications. We extend the technique and result to the real case.