Semialgebraic universal covers of normal projective varieties

OpenAI

A connected normal complex projective variety has a universal cover biholomorphic to a semialgebraic open subset of a projective variety exactly when that cover is D×C^m×F, with D a bounded symmetric domain and F simply connected, normal and projective.

Sources for this record

What was already known

Kollár and Pardon proved a nonabelian lattice case and a fiber-bundle theorem, then posed the broader product classification.

AI involvement AI-led

OpenAI is the named manuscript author. The release says its manuscripts and supporting artifacts were produced by an internal OpenAI model, which supports AI-led involvement by institutional authorship, without establishing no human mathematical input.

The specific paper names OpenAI as author, and the release describes internal-model-produced manuscripts.

Importance Notable

Would settle the normal-projective Kollár–Pardon classification.

Limitations

The available Lean proof addresses a companion bounded-domain symmetry theorem, not this product classification. No completed check or named human explanation of the classification is documented; its proof depends on other newly claimed results.

Technical verification Reported

The cited Lean Comparator and proof endpoint formalize the companion bounded-domain symmetry statement, not the universal-cover product classification. No completed check of Theorem 1.1 was documented in the inspected release; Reported is the evidence default.

Human understanding Few

The AI-authored manuscript gives a proof outline, but no named person's understanding of its central boundary and Albanese mechanisms is documented; Few is the evidence default.

Correction and publication history