Intersection theory on surfaces

This thesis studies intersection theory on projective surfaces with isolated singularities. We review the classical intersection theory on a nonsingular surface, proceed to an overview of types of singularity that may arise, and then discuss the intersection theory of Snapper-Kleiman, that of Reeve-Tyrrell, and a modification of the latter that we propose.The intersection theory of Snapper-Kleiman applies to varieties of any dimension but is restricted to locally principal divisors; that of Reeve-Tyrrell applies to arbitrary divisors but is restricted to surfaces. Our modification has the same domain of application as the theory of Reeve-Tyrrell but simplifies computations: it allows us to prove the theories are all equivalent on normal surfaces. We finish by developing generalizations of the main theorems on nonsingular surfaces