Chern currents of coherent sheaves
| Autor: | Lärkäng, Richard, Wulcan, Elizabeth |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Ãpijournal de Géométrie Algébrique, Volume 6 (July 30, 2022) epiga:8653 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.46298/epiga.2022.8653 |
| Popis: | 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. Comment: 26 pages. v5: Correct \'Epiga article number, no other change to v3 |
| Databáze: | arXiv |
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