Limits of Chow groups, and a new construction of Chern-Schwartz-MacPherson classes
Algebraic Geometry
2012-04-11 v2
Abstract
We define an `enriched' notion of Chow groups for algebraic varieties, agreeing with the conventional notion for complete varieties, but enjoying a functorial push-forward for arbitrary maps. This tool allows us to glue intersection-theoretic information across elements of a stratification of a variety; we illustrate this operation by giving a direct construction of Chern-Schwartz-MacPherson classes of singular varieties, providing a new proof of an old (and long since settled) conjecture of Deligne and Grothendieck.
Keywords
Cite
@article{arxiv.math/0507029,
title = {Limits of Chow groups, and a new construction of Chern-Schwartz-MacPherson classes},
author = {Paolo Aluffi},
journal= {arXiv preprint arXiv:math/0507029},
year = {2012}
}
Comments
23 pages, final version. Dedicated to Robert MacPherson on the occasion of his 60th birthday