Some Differential Properties in the Large of Algebraic Curves, their Intersections, and Self-correspondences

Abstract

We shall show in the present Part how the theory of residues of analytic functions can be employed in the — local or global — study of certain differential properties of analytic and algebraic curves; these properties will concern differential elements defined by intersections, or by fixed points of analytic or algebraic correspondences. Further, with regard to the above theory, intrinsic geometric interpretations will be introduced, which will imply geometric meanings for the differential invariants as they arise.