Deformation-obstruction theory for complexes via Atiyah and Kodaira-Spencer classes
Deformation-obstruction theory for complexes via Atiyah and Kodaira-Spencer classes
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Atiyah 和 Kodaira-Spencer 类复合体的变形阻碍理论
DOI：
10.1007/s00208-009-0397-6
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发表时间：
2009
影响因子：
1.4
通讯作者：
Huybrechts D
中科院分区：
文献类型：
--
作者：
Huybrechts D
本文给出了光滑射影族上凝聚层的导出范畴的物体的变形-阻塞理论的一个普遍的方法。我们恢复和推广Lowen和Lieblich的阻塞类，并证明它是Atiyah和Kodaira-Spencer类的产物。这使我们能够获得变形不变的虚拟循环模空间的对象的衍生类别上的三倍。
We give a universal approach to the deformation-obstruction theory of objects of the derived category of coherent sheaves over a smooth projective family. We recover and generalise the obstruction class of Lowen and Lieblich, and prove that it is a product of Atiyah and Kodaira–Spencer classes. This allows us to obtain deformation-invariant virtual cycles on moduli spaces of objects of the derived category on threefolds.