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- W4286770112 abstract "Given a finite locally free resolution of a coherent analytic sheaf $mathcal F$, equipped with Hermitian metrics and connections, we construct an explicit current, obtained as the limit of certain smooth Chern forms of $mathcal F$, that represents the Chern class of $mathcal F$ and has support on the support of $mathcal F$. If the connections are $(1,0)$-connections and $mathcal F$ has pure dimension, then the first nontrivial component of this Chern current coincides with (a constant times) the fundamental cycle of $mathcal F$. The proof of this goes through a generalized Poincar'e-Lelong formula, previously obtained by the authors, and a result that relates the Chern current to the residue current associated with the locally free resolution." @default.
- W4286770112 created "2022-07-23" @default.
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- W4286770112 date "2021-05-31" @default.
- W4286770112 modified "2023-10-17" @default.
- W4286770112 title "Chern currents of coherent sheaves" @default.
- W4286770112 doi "https://doi.org/10.48550/arxiv.2105.14843" @default.
- W4286770112 hasPublicationYear "2021" @default.
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