The enumeration of simultaneous higher-order contacts between plane curves

Abstract

Using the Semple bundle construction, we derive an intersection-theoretic formula for the number of simultaneous contacts of specified orders between members of a generic family of degree $d$ plane curves and finitely many fixed curves. The contacts counted by the formula occur at nonsingular points of both the members of the family and the fixed curves.Comment: 32 pages, AmS-TeX v2.1 (Revised statement and proof of one lemma; other minor changes.