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

Alexey Bondal; Alexei Rosly

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arXiv · 2211.11112

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

Alexey Bondal·Alexei Rosly

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Abstract

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.

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Alexey Bondal, Alexei Rosly. 2022-11-20. Coherent Sheaves, Chern Classes, and Superconnections on Compact Complex-Analytic Manifolds. https://arxiv.org/abs/2211.11112

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