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A vanishing theorem on fake projective planes with enough automorphisms
For every fake projective plane with automorphism group of order 21, we
prove that for all and for every ample line bundle with
. For every fake projective plane with automorphism group of order 9, we
prove the same vanishing for every cubic root (and its twist by a 2-torsion) of
the canonical bundle . As an immediate consequence, there are exceptional
sequences of length 3 on such fake projective planes.Comment: 17 page
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