Explicit equations are constructed for two new pairs of fake projective planes with 21 automorphisms via Dolgachev elliptic surfaces with double and triple fibers.
Ishida, An elliptic surface covered by Mumford's fake projective plane, Tohoku Math
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On equations of fake projective planes with automorphism group of order $21$
Explicit equations are constructed for two new pairs of fake projective planes with 21 automorphisms via Dolgachev elliptic surfaces with double and triple fibers.