New explicit constructions of surfaces of general type

2020/04/06 by Borisov, Lev, Fatighenti, Enrico · 1 citation
#14J29 14J29 14J29 #14Q10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2004.02637

Abstract

We discover a simple construction of a four-dimensional family of smooth surfaces of general type with p_g(S)=q(S)=0, K²_S=3 with cyclic fundamental group C₁₄. We use a degeneration of the surfaces in this family to find (complicated) explicit equations of six new pairs of fake projective planes. Our methods for finding new fake projective planes involve nontrivial computer calculations which we hope will be applicable in other settings.

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• Finding equations of the fake projective plane (C18,p=3,\2I\)

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