Mathematics – Algebraic Geometry
Scientific paper
2005-07-01
Pure Appl. Math. Q. 2 (2006), no. 4, part 2, 915-941
Mathematics
Algebraic Geometry
23 pages, final version. Dedicated to Robert MacPherson on the occasion of his 60th birthday
Scientific paper
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.
Aluffi Paolo
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