# Jet differentials and hyperbolicity: possible mistake in the literature?

I was reading this note by Jingzhou Sun http://arxiv.org/abs/1109.1329 about Demailly's approach to hyperbolicity using jet differentials. The author seems to claim that there is a mistake in one of Demailly's early papers on the subject, and even shows a calculation that apparently contradicts a classical result of Demailly-El Goul (and potentially many other later works based on this approach).

More specifically, he claims that there are two definitions of the bundle of $k$-jet differentials of weighted degree $m$ which people assumed were equivalent, but which in fact are not the same.

Has anybody looked at this note? Is the objection raised by the author justified?

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I find it hard to believe that there is really a crucial mistake in the work of Demailly et al. It seems more likely that Sun's paper is not quite correct. I am particularly worried by the sentence "One can then compute... and see...". – YangMills Apr 19 '13 at 18:28