Intersection theory: watching the movie instead of counting the characters

Resumen:

Quite often in intersection theory, in order to define the intersection number of two subvarieties at a point p, one puts the two subvarieties "in general position" by a one parameter deformation, and then counts the number of the -now transversal- intersection points which coalesce to the original point p as the parameter vanishes. I will present situations where it is useful to distinguish the different "speeds" at which the intersection points tend to p as the deformation parameter tends to 0.

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