Toward a geometric construction of fake projective planes
JongHae Keum

TL;DR
This paper provides a geometric criterion for identifying when a projective surface is a quotient of a fake projective plane, along with detailed analysis of related elliptic fibrations and classifications of certain rational surfaces.
Contribution
It introduces a new geometric criterion for recognizing quotients of fake projective planes and classifies specific rational surfaces with cusps.
Findings
Criterion for a surface to be a quotient of a fake projective plane
Detailed description of elliptic fibrations of related surfaces
Classification of ${f Q}$-homology projective planes with cusps
Abstract
We give a criterion for a projective surface to become a quotient of a fake projective plane. We also give a detailed information on the elliptic fibration of a -elliptic surface that is the minimal resolution of a quotient of a fake projective plane. As a consequence, we give a classification of -homology projective planes with cusps only.
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