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An algebraic characterization of distinguished varieties of intersection. (English) Zbl 0807.14003
One gives a characterization of the components of the Stückrad-Vogel intersection cycle of two pure-dimensional closed subschemes in the projective space, using the theory of reductions of Northcott-Rees. One obtains a local variant of a result of Van Gastel about the relationship between the (excess) intersection theory of Fulton and MacPherson and the theory of excess intersections in the projective space, developed by Stückrad and Vogel.

14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
13H15 Multiplicity theory and related topics
13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series