A Generalized Grothendieck-RIemann-Roch Theorem for Hirzebruch's χy-Characteristic and Ty-Characteristic
A Generalized Grothendieck-RIemann-Roch Theorem for Hirzebruch's χy-Characteristic and Ty-Characteristic
复制标题
Hirzebruch χy 特征和 Ty 特征的广义 Grothendieck-Riemann-Roch 定理
DOI：
10.2977/prims/1195165791
复制
发表时间：
1994
影响因子：
1.2
通讯作者：
Shoji Yokura
中科院分区：
文献类型：
--
作者：
Shoji Yokura
Grothendieck-Riemann-Roch（缩写 GRR）是 Hirzebruch-Riemann-Roch（缩写 HRR）的相对版本，%(X, E)=T(X, E)。 Hirzebruch 的 %y 特征 Xy(X, E) 和 ^-特征 Ty(X, E) 是 Euler-Poincare 特征 %(X, E) 和 Todd 特征 T(X, £*) 的推广，这样当 >? = 0 Xo(X, E) = %(X, £) 且 T0(X, £) =T(X, £)，且它们相等； Xy(X, E} = Ty(X, E)，称为广义 Hirzebruch-Riemann-Roch（缩写 g-HRR）。在这篇简短的说明中，我们表明我们可以获得一个广义 GRR 版本（缩写 g-GRR），这样当 y = 0 时，我们的 g-GRR 专门针对原始 GRR，并且通过将 X 映射到一点，从 g-GRR 导出 Hirzebruch 的 g-HRR，就像 HRR 是通过将 X 映射到一个点而从 GRR 导出的一样。有关我们主要定理的陈述和证明，请参见第 2 节。
The Grothendieck-Riemann-Roch (abbr. GRR) is a relative version of the Hirzebruch-Riemann-Roch (abbr. HRR), %(X, E)=T(X, E). Hirzebruch's %ycharacteristic Xy(X, E) and ^-characteristic Ty(X, E) are a generalization of the Euler-Poincare characterisitc %(X, E) and the Todd characteristic T(X, £*) such that when>? = 0 Xo(X, E) = %(X, £) and T0(X, £) =T(X, £), and they are equal; Xy(X, E} = Ty(X, E), which is called the generalized Hirzebruch-Riemann-Roch (abbr. g-HRR). In this short note we show that we can get a generalized GRR version (abbr. g-GRR) such that when y = 0 our g-GRR specializes to the original GRR and such that the Hirzebruch's g-HRR is induced from our g-GRR by mapping X to a point, just like HRR is induced from GRR by mapping X to a point. For the statements and the proofs of our main theorems see § 2.