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

2022/11/20 by Alexey Bondal, Bondal, Alexey, A. A. Rosly +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2211.11112

openalex publication_date 2022/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ∂-superconnections. Then we apply the techniques of ∂-superconnections to define Chern classes and Bott-Chern classes of objects in the category, in particular, of coherent sheaves.

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