Canonical rational equivalence of intersections of divisors
Abstract
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).
- Publication:
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arXiv e-prints
- Pub Date:
- October 1997
- DOI:
- 10.48550/arXiv.alg-geom/9710011
- arXiv:
- arXiv:alg-geom/9710011
- Bibcode:
- 1997alg.geom.10011K
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14C17
- E-Print:
- LaTeX2e, 14 pages