A higher-order contract formula for plane curves
We drive an intersection-theoretic formula for the number of nth-order contacts between a given (n-1)-parameter family of plane curves and a gerenal specified curve. This is accomplished through the use of a tower of P 1-budles first introduced by Semple in [Se]. These bundles may be seen to parameterize nth-order curvilinear contact at a point in a natural way.
Colley, Susan Jane, and Gary Kennedy. 1991. "A higher-order contract formula for plane curves." Communications in Algebra 19(2): 479-508.
Taylor & Francis
Communications in Algebra