Geodesic
Coherent sheaves, Chern classes, and superconnections
Izvestiya. Mathematics , Tome 87 (2023) no. 3, pp. 439-468.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: coherent sheaves, derived category, DG-category, Dolbeault operator, superconnection. 
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A. I. Bondal; A. A. Roslyi. Coherent sheaves, Chern classes, and superconnections. Izvestiya. Mathematics , Tome 87 (2023) no. 3, pp. 439-468. http://geodesic.mathdoc.fr/item/IM2_2023_87_3_a2/

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