Pith. sign in

REVIEW 1 cited by

New explicit constructions of surfaces of general type

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2004.02637 v2 pith:YU6JWYDE submitted 2020-04-06 math.AG

Lev Borisov , Enrico Fatighenti This is my paper · ORCID
classification math.AG
keywords surfacesexplicitfakefamilygeneralplanesprojectivetype
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We discover a simple construction of a four-dimensional family of smooth surfaces of general type with $p_g(S)=q(S)=0$, $K^2_S=3$ with cyclic fundamental group $C_{14}$. 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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Finding equations of the fake projective plane $(C18,p=3,\{2I\})$

    math.AG 2025-12 conditional novelty 5.0 of 10

    Explicit bicanonical equations are produced for the fake projective plane (C18,p=3,{2I}), adding the 12th pair of fake projective planes to the list of those with known equations.

Pith tools