Duality and intersection theory in complex manifolds. I
Duality and intersection theory in complex manifolds. I
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复流形中的对偶性和交集理论。
DOI：
10.1007/bf01351557
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发表时间：
1978
影响因子：
1.4
通讯作者：
Y. L. Tong
中科院分区：
文献类型：
--
作者：
D. Toledo;Y. L. Tong
我们引入了扭曲上链和凝聚层的扭曲复形的概念。对于子流形的层，这些扭曲复形被用来在余链水平上构造对偶类的Grothendieck理论和Gysin映射。例如，这些显式构造给出了对偶类高余维子流形的局部公式。我们使用这样的局部公式证明了Hirzebruch Riemann Roch的一个精化版本。我们还证明了一个关于何时可以从一阶几何数据计算全局解析交类的定理。这一理论将被用来证明解析相干层的全纯Lefschetz公式(第二部分)和Hirzebruch Riemann Roch。
We introduce the concept of a twisting cochain and a twisted complex associated to a coherent sheaf. For sheaves of submanifolds these twisted complexes are used to construct on cochain level the Grothendieck theory of dual class and Gysin map. These explicit constructions give, for instance, a local formula for dual class of higher codimensional submanifolds. We prove a refined version of the Hirzebruch Riemann Roch using such local formulas. We also prove a theorem on when global analytic intersection classes can be computed from first order geometric data. This theory will be used to prove the Holomorphic Lefschetz formula (in Part II) and the Hirzebruch Riemann Roch for analytic coherent sheaves.