Limits of Chow groups, and a new construction of Chern-Schwartz-MacPherson classes
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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- July 2005
- DOI:
- arXiv:
- arXiv:math/0507029
- Bibcode:
- 2005math......7029A
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14C17;
- 57D20
- E-Print:
- 23 pages, final version. Dedicated to Robert MacPherson on the occasion of his 60th birthday