Coherent Sheaves, Chern Classes, and Superconnections on compact complex-analytic manifolds

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  • Authors: Bondal A.I.1,2,3, Rosly A.A.4,5,6
  • Affiliations:
    1. Steklov Mathematical Institute of Russian Academy of Sciences
    2. Moscow Institute of Physics and Technology (National Research University)
    3. Kavli Institute for the Physics and Mathematics of the Universe
    4. Skolkovo Institute of Science and Technology
    5. Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute)
    6. HSE University
  • Issue: Vol 87, No 3 (2023)
  • Pages: 23-55
  • Section: Articles
  • URL: https://journals.rcsi.science/1607-0046/article/view/133907
  • DOI: https://doi.org/10.4213/im9386
  • ID: 133907

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Abstract

We construct a twist-closed enhancement of the category $\mathcal D^b_{coh}(X)$, the boundedderived category of complexes of $\mathcal O_X$-modules with coherent cohomology, by meansof the DG-category of $\bar\partial$-superconnections. Then we apply the techniques of $\bar\partial$-superconnections to dene Chern classes and Bott–Chern classes of objects in the category, in particular, of coherent sheaves.

About the authors

Alexey Igorevich Bondal

Steklov Mathematical Institute of Russian Academy of Sciences; Moscow Institute of Physics and Technology (National Research University); Kavli Institute for the Physics and Mathematics of the Universe

Email: bondal@mi-ras.ru
Doctor of physico-mathematical sciences

Alexei Andreevich Rosly

Skolkovo Institute of Science and Technology; Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute); HSE University

Email: rosly@itep.ru
Candidate of physico-mathematical sciences

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