Mathematical Research Letters

Volume 22 (2015)

Number 1

Exceptional collections on 2-adically uniformized fake projective planes

Pages: 43 – 57



Najmuddin Fakhruddin (School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India)


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.

Accepted 14 May 2014

Published 13 April 2015