Equivariant Chern classes of singular algebraic varieties with group actions
Equivariant Chern classes of singular algebraic varieties with group actions
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DOI：
10.1017/s0305004105008820
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发表时间：
2004-07
影响因子：
0.8
通讯作者：
T. Ohmoto
中科院分区：
文献类型：
--
作者：
T. Ohmoto
我们定义一个可能奇异的代数$G$-簇在基域$\mathbb{C}$上的等变陈施瓦茨麦克弗森类，或者更一般地在特征为0的域上。实际上，我们构造了一个从$G$-等变可构造函数函子$\cal{F}^G$到$G$-等变同调函子$H^G_*$或$A^G_*$（在Totaro-Edidin-Graham意义下）的自然变换$C^G_*$。这个$C^G_*$可以被认为是（某些）商栈的麦克弗森变换。Verdier-Riemann-Roch公式在整个过程中起着关键作用。
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.