Canonical rational equivalence of intersections of divisors
نویسنده
چکیده
We consider the operation of intersecting with a locally principal Cartier divisor (i.e., a Cartier divisor which is principal on some neighborhood of its support). We describe this operation explicitly on the level of cycles and rational equivalences and as a corollary obtain a formula for rational equivalence between intersections of two locally principal Cartier divisors. Such canonical rational equivalence applies quite naturally to the setting of algebraic stacks. We present two applications: (i) a simplification of the development of Fulton-MacPherson-style intersection theory on Deligne-Mumford stacks, and (ii) invariance of a key rational equivalence under a certain group action (which is used in developing the theory of virtual fundamental classes via intrinsic normal cones). DOI: Canonical rational equivalence of intersections of divisors Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: http://doi.org/10.5167/uzh-22142 Accepted Version Originally published at: Kresch, A (1999). Canonical rational equivalence of intersections of divisors. Inventiones Mathematicae, 136(3):483-496. DOI: Canonical rational equivalence of intersections of divisors ar X iv :a lg -g eo m /9 71 00 11 v2 4 D ec 1 99 7 Canonical rational equivalence of intersections of divisors
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