Universal additive Chern classes and a GRR-type theorem

Equivariant Chern classes and localization theorem

For a complex variety with a torus action we propose a new method of computing Chern-Schwartz-MacPherson classes. The method does not apply resolution of singularities. It is based on the Localization Theorem in equivariant cohomology. This is an extended version of the talk given in Hefei in July 2011.

A generalized Verdier-type Riemann-Roch theorem for Chern-Schwartz-MacPherson classes

In this paper we give a general formula for the defect appearing in the Verdiertype Riemann-Roch formula for Chern-SchwartzMacPherson classes in the case of a regular embedding (and for suitable local complete intersection morphisms). Our proof of this formula uses the ”constructible function version” of Verdier’s specialization functor SpX\Y (for constructible (complexes of) sheaves), together...

Finitely Additive Beliefs and Universal Type Spaces

In this paper we examine the existence of a universal (to be precise: terminal) type space when beliefs are described by finitely additive probability measures. We find that in the category of all type spaces that satisfy certain measurability conditions (κ-measurability, for some fixed regular cardinal κ), there is a universal type space (i.e. a terminal object, that is a type space to which e...

Chow Homology and Chern Classes

Stringy Chern classes

Work of Dixon, Harvey, Vafa and Witten in the 80’s ([DHVW85]) introduced a notion of Euler characteristic (for quotients of a torus by a finite group) which became known as the physicist’s orbifold Euler number. In the 90’s V. Batyrev introduced a notion of stringy Euler number ([Bat99b]) for ‘arbitrary Kawamata log-terminal pairs’, proving that this number agrees with the physicist’s orbifold ...