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).
Keywords
Cite
@article{arxiv.alg-geom/9710011,
title = {Canonical rational equivalence of intersections of divisors},
author = {Andrew Kresch},
journal= {arXiv preprint arXiv:alg-geom/9710011},
year = {2016}
}
Comments
LaTeX2e, 14 pages; expanded intro; new first section fixes some errors