Applications of Residue Theory to Curves

Abstract

The formulas and theorems in Chapter 11 on residues in the affine plane allow uniform proofs and generalizations of classical theorems about intersection theory of plane curves. Maybe B. Segre [Se] was the first who proceeded in a way similar to ours, but he used another concept of residue, the residue of differentials on a smooth curve. See also Griffiths-Harris [GH], Chapter V. The theorems presented here have far-reaching higher-dimensional generalizations ([Hü],[HK], [Ku₃],[Ku₄], [KW]). In his thesis [Q] Gerhard Quarg has discovered further global geometric applications of algebraic residue theory. [Ku₄] contains an outline of part of this thesis.