We discover a simple construction of a four-dimensional family of smooth surfaces of general type with pg(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.
Borisov, L., Fatighenti, E. (2026). New explicit constructions of surfaces of general type. JOURNAL OF ALGEBRAIC GEOMETRY, 35, 197-224 [10.1090/jag/857].
New explicit constructions of surfaces of general type
Fatighenti, Enrico
2026
Abstract
We discover a simple construction of a four-dimensional family of smooth surfaces of general type with pg(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.File in questo prodotto:
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FPP-C14-paper.pdf
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