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Celestial Integration, Stringy Invariants, and Chern-Schwartz-MacPherson Classes

  • Paolo Aluffi
Part of the Trends in Mathematics book series (TM)

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.

Keywords

Zeta Function Chern Class Inverse Limit Chow Group Chern Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Paolo Aluffi
    • 1
  1. 1.Mathematics DepartmentFlorida State UniversityTallahasseeUSA

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