Celestial integration, stringy invariants, and Chern-Schwartz-MacPherson classes
arXiv:math/0506608 · doi:10.1007/978-3-7643-7776-2_1
Abstract
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.
11 pages, LaTeX