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11. Mirror construction for fake projective planes

How to find (algebraically, say) a mirror construction for fake projective planes (certain rigid surface of general type with same Hodge numbers as projective space, otherwise very different).

$\bullet$ There exist 100 of them, but only 22 have known explicit equations. $\bullet$ Not complete intersections

      Cite this as: AimPL: Syzygies and mirror symmetry, available at http://aimpl.org/syzygyms.