Celestial integration, stringy invariants, and Chern-Schwartz-MacPherson classes

Details Celestial integration, stringy invariants, and Chern-Schwartz-MacPherson classes Celestial integration, stringy invariants, and Chern-Schwartz-MacPherson classes

2005-06-29

arxiv.org/abs/math/0506608v1

Real and complex singularities, 1-13, Trends Math., Birk\"auser, Basel, 2007

Mathematics

Algebraic Geometry

11 pages, LaTeX

Scientific paper

10.1007/978-3-7643-7776-2_1

We introduce a formal integral on the system of varieties mapping properly and birationally to a given one, with value in an associated Chow group. Applications include comparisons of Chern numbers of birational varieties, new birational invariants, `stringy' Chern classes, and a `celestial' 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. The formalism has points of contact with motivic integration.

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