Abstract.
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.
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Aluffi, P. Modification systems and integration in their Chow groups. Sel. math., New ser. 11, 155 (2005). https://doi.org/10.1007/s00029-005-0004-y
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DOI: https://doi.org/10.1007/s00029-005-0004-y