Header

UZH-Logo

Maintenance Infos

Canonical rational equivalence of intersections of divisors


Kresch, A (1999). Canonical rational equivalence of intersections of divisors. Inventiones Mathematicae, 136(3):483-496.

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).

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).

Statistics

Citations

14 citations in Web of Science®
16 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

25 downloads since deposited on 29 Nov 2010
8 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1999
Deposited On:29 Nov 2010 16:27
Last Modified:05 Mar 2017 08:23
Publisher:Springer
ISSN:0020-9910
Publisher DOI:https://doi.org/10.1007/s002220050317
Related URLs:http://arxiv.org/abs/alg-geom/9710011

Download

Download PDF  'Canonical rational equivalence of intersections of divisors'.
Preview
Content: Accepted Version
Filetype: PDF
Size: 154kB
View at publisher