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Sep 9, 2020 at 23:10 comment added Evgeny Shinder For singular curves, the nontrivial part of $K_0(X)$ should come from the Picard group $Pic(X)$ which can be computed in terms of the local structure of singular points. One reference about Picard group of singular curves is link.springer.com/content/pdf/10.1007/BF01440949.pdf.
Sep 3, 2020 at 4:45 history asked user127776 CC BY-SA 4.0