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Limits of Chow groups, and a new construction of Chern-Schwartz-MacPherson classes

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.

preprint2006arXivOpen access
Paolo Aluffi
math.AG
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Paolo Aluffi

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