Equivariant Chern classes of singular algebraic varieties with group actions

By Toru Ohmoto. Mathematical Proceedings of the Cambridge Philosophical Society, 2004

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We define equivariant Chern–Schwartz–MacPherson classes of a possibly singular algebraic $G$-variety over the base field $\mathbb{C}$, or more generally over a field of characteristic 0. In fact, we construct a natural transformation $C^G_*$ from the $G$-equivariant constructible function functor $\cal{F}^G$ to the $G$-equivariant homology functor $H^G_*$ or $A^G_*$ (in the sense of Totaro–Edidin–Graham). This $C^G_*$ may be regarded as MacPherson's transformation for (certain) quotient stacks. The Verdier–Riemann–Roch formula takes a key role throughout.

Subfields: Geometry and Topology, Mathematical Physics

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