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 FultonMacPhersonstyle intersection theory on DeligneMumford 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:

arXiv eprints
 Pub Date:
 October 1997
 DOI:
 10.48550/arXiv.alggeom/9710011
 arXiv:
 arXiv:alggeom/9710011
 Bibcode:
 1997alg.geom.10011K
 Keywords:

 Mathematics  Algebraic Geometry;
 14C17
 EPrint:
 LaTeX2e, 14 pages