Kavli Affiliate: Alexey Bondal
| Summary:
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 $barpartial$-superconnections. Then we apply the techniques of $barpartial$-superconnections to define Chern classes and Bott-Chern classes of objects in the category, in particular, of coherent sheaves.
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