The enumeration of simultaneous higher-order contacts between plane curves

1992/12/08 by Susan Jane Colley, Colley, Susan Jane, Gary Kennedy +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9212003

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

arxiv created 1993/06/30 · arxiv updated 2009/11/30

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.

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