Equivariant Chern classes of singular algebraic varieties with group actions

Abstract

We define the equivariant Chern-Schwartz-MacPherson class of a possibly singular algebraic variety with a group action over the complex number field (or a field of characteristic 0). In fact, we construct a natural transformation from the equivariant constructible function functor to the equivariant homology functor (in the sense of Totaro-Edidin-Graham), which may be regarded as MacPherson's transformation for (certain) quotient stacks. We discuss on other type Chern/Segre classes and give some applications generalizing orbifold Euler characteristics and Thom polynomials of singularities. The Verdier-Riemann-Roch formula takes a key role throughout.

AMS-LaTeX, 30 pages, no figure

References in corpus (4)

• A generalized Verdier-type Riemann-Roch theorem for Chern-Schwartz-MacPherson classes
• Stringy Chern classes of singular varieties
• Chern classes of proalgebraic varieties and motivic measures
• Calculation of Thom polynomials for group actions

Cited by in corpus (21)

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• Chern Classes of Open Projected Richardson Varieties and of Affine Schubert Cells
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