Exceptional collections on 2-adically uniformized fake projective planes

We show that there exist exceptional collections of length $3$ consisting of line bundles on the three fake projective planes that have a $2$-adic uniformization with torsion-free covering group. We also compute the Hochschild cohomology of the right orthogonal of the subcategory of the bounded derived category of coherent sheaves generated by these exceptional collections.

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Accepted 14 May 2014

Published 13 April 2015