Abstract:
A twist-closed enhancement of the bounded derived category
$\mathcal{D}^b_{\mathrm{coh}} (X)$
of complexes of $\mathcal{O}_X$-modules
with coherent cohomology is constructed by means of the DG-category of
$\overline\partial$-superconnections. The machinery of
$\overline\partial$-superconnections is applied to define Chern classes and
Bott–Chern classes of objects in the category, in particular,
of coherent sheaves.
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