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Jul 17, 2016 at 5:45 comment added Sasha It is probably a direct sum as $p_1^{-1}O_X$-module, but not as $O_{X\times X}$-module. And in the Remark after the proof the Atiyah class is explicitly mentioned.
Jul 16, 2016 at 23:40 comment added A Rock and a Hard Place Thanks, this makes a lot more sense. Though the cited paper of KS does pretty explicitly claim $P_k$ to be a direct sum ... I guess just about every paper has a typo.
Jul 16, 2016 at 23:40 vote accept A Rock and a Hard Place
Jul 16, 2016 at 13:28 history answered Sasha CC BY-SA 3.0