Toward a geometric construction of fake projective planes

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 $(2,3)$-elliptic surface that is the minimal resolution of a quotient of a fake projective plane. As a consequence, we give a classification of $\mathbb{Q}$-homology projective planes with cusps only.

14 pages. Minor changes in Theorem 0.6 and Remark 0.7 were made