Riemann-roch for singular varieties
Riemann-roch for singular varieties
复制标题
奇异簇的 Riemann-roch
DOI：
10.1007/bf02684299
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发表时间：
1975
期刊：
影响因子：
--
通讯作者：
R. Macpherson
中科院分区：
文献类型：
--
作者：
P. Baum;W. Fulton;R. Macpherson
The basic tool for a general Riemann-Roch theorem is MacPherson’s graph construction, applied to a complex E. of vector bundles on a scheme Y, exact off a closed subset X. This produces a localized Chern character1 ch x y (E.) which lives in the bivariant group \( A{\left( {X \to Y} \right)_\mathbb{Q}} \) For each class α∈A * Y, this gives a class
$$ ch_X^Y\left( {E.} \right) \cap \alpha \in {A_ * }{X_\mathbb{Q}} $$
whose image in \( {A_ * }{Y_\mathbb{Q}} \) is \( {\sum {\left( { - 1} \right)} ^i}ch\left( {{E_i}} \right) \cap \alpha \) The properties needed for Riemann-Roch, in particular the invariance under rational deformation, follow from the bivariant nature of ch x y E.
The basic tool for a general Riemann-Roch theorem is MacPherson’s graph construction, applied to a complex E. of vector bundles on a scheme Y, exact off a closed subset X. This produces a localized Chern character1 ch x y (E.) which lives in the bivariant group \( A{\left( {X \to Y} \right)_\mathbb{Q}} \) For each class α∈A * Y, this gives a class
$$ ch_X^Y\left( {E.} \right) \cap \alpha \in {A_ * }{X_\mathbb{Q}} $$
whose image in \( {A_ * }{Y_\mathbb{Q}} \) is \( {\sum {\left( { - 1} \right)} ^i}ch\left( {{E_i}} \right) \cap \alpha \) The properties needed for Riemann-Roch, in particular the invariance under rational deformation, follow from the bivariant nature of ch x y E.