2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101277A fake projective plane is a compact complex manifold of dimension 2 which has the same Betti numbers as the complex projective plane, but not isomorphic to the complex projective plane. As was shown by D. Mumford, there exists at least one such surface. In this paper we prove the existence of a fake projective plane which is birational to a cyclic cover of degree 7 of a Dolgachev surface.An error in the previous version has been corrected. 9 pagesAlgebraic GeometryAlgebraic Topology14J29text