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.

32 pages, AmS-TeX v2.1 (Revised statement and proof of one lemma; other minor changes.)

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