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Title:
D-bar superconnections and coherent sheaves
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Abstract:
We construct a DG-enhancement of the derived category of coherent sheaves in differential geometrical terms. This construction generalizes the description of holomorphic bundles as flat $\bar\partial$-connections to the case of sheaves and uses the notion of a superconnection (in the sense of Quillen). It works on smooth complex analytic (not necessarily algebraic) manifolds. As a byproduct, we obtain a construction of Chern classes of coherent sheaves.
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