相干层、超连接与RRG

Coherent Sheaves, Chern Classes, and Superconnections on Compact Complex-Analytic Manifolds

We construct a twist-closed enhancement of the category ${\mathcal D}^b_{\rm coh}(X)$, the bounded derived category of complexes of ${\mathcal O}_X$-modules with coherent cohomology, by means of the DG-category of $\bar\partial$-superconnections. Then we apply the techniques of $\bar\partial$-superconnections to define Chern classes and Bott-Chern classes of objects in the category, in particular, of coherent sheaves.

On the Bott-Chern characteristic classes for coherent sheaves

Using the concept of a cohesive module defined by Block, we use the theory of superconnections in the sense of Quillen to construct natural superconnections on Hermitian cohesive modules. By the Chern-Weil construction, we obtain characteristic classes with values in Bott-Chern cohomology which refines the usual deRham cohomology. The main result of this paper shows that such characteristic classes are independent of the Hermitian metric and only dependent on the homotopy class of the cohesive module in the homotopy category. This extends the Bott-Chern cohomology to the bounded derived catego…

横全纯叶状结构上的超联络、下降与单值性

Superconnections, descent, and monodromy on transversely holomorphic foliations

本文针对横全纯叶状结构构造凝聚O_V模导出范畴的有限超联络模型，证明其与有界有限秩平坦V-超联络同伦范畴等价，还研究了下降性、单值群胚关联及全纯悬链相关性质。

紧致复流形上凝聚模的形变

Deformations of cohesive modules on compact complex manifolds

本文研究紧致复流形上凝聚模的形变理论，推广了全纯向量丛和凝聚层的形变，并发展了Kuranishi映射与障碍理论，给出了无阻碍形变的例子。