Modification systems and integration in their Chow groups

Details Modification systems and integration in their Chow groups Modification systems and integration in their Chow groups

2004-07-08

arxiv.org/abs/math/0407150v2

Selecta Math. (N.S.) 11 (2005), no. 2, 155-202

Mathematics

Algebraic Geometry

42 pages, LaTeX, 2 figures

Scientific paper

10.1007/s00029-005-0004-y

We introduce a notion of integration on the category of proper birational maps to a given variety $X$, with value in an associated Chow group. Applications include new birational invariants; comparison results for Chern classes and numbers of nonsingular birational varieties; `stringy' Chern classes of singular varieties; and a zeta function specializing to the topological zeta function. In its simplest manifestation, the integral gives a new expression for Chern-Schwartz-MacPherson classes of possibly singular varieties, placing them into a context in which a `change-of-variable' formula holds. v2: References added, and overly optimistic claims concerning non log-terminal singularities expunged.

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