I'm used to seeing phrases like "in dimensions 3 or 4" or "for dimensions 5 and up" but I've never seen "up to complex dimension 77" before https://arxiv.org/abs/1903.10043
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Replying to @sigfpe
It's interesting but frustrating to see how the number 77 sneaks in on page 7 of this paper, which starts out as "beautiful abstract generalities". The author, a student, does a couple of calculations that are probably rather easy a bit too quickly to follow them step-by-step.
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Replying to @johncarlosbaez
Not having read the paper I wonder if 77 is just an artifact of the proof method or corresponds to a property of an actual manifold. (Like how the Riemann-Hurwitz formula leads you to 168 but that turns out to correspond to the automorphisms of an actual Riemann surface.)
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Replying to @sigfpe @johncarlosbaez
So far as I can tell, 77 appears because it's the largest positive integer where -n^3+77n^2+12n is positive (Lemma 3.2), and this polynomial is apparently dim W - rank E - k, for a certain k-ample vector bundle E over a compact complex manifold W (Lemma 3.1).
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Sorry, that should be Theorem 3.1 in the last tweet. Not clear to me (very non-expert) whether this is best possible or if this could somehow be improved.
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