What was already known
Kollár and Pardon posed this bounded semialgebraic affine-domain question while studying varieties with semialgebraic universal covers. The compact quotient gives uniformity but does not assume a transitive automorphism group (companion manuscript introduction, pp. 1–2).
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Answers the bounded-domain symmetry question of Kollár and Pardon.
Limitations
The selected theorem concerns bounded semialgebraic affine domains with proper compact-quotient group action; it does not by itself classify all semialgebraic universal covers of projective varieties. Finite stabilizers and singular affine ambient varieties are allowed.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note formalizes smoothness and bounded symmetric-domain structure under the stated proper cocompact action, allowing finite stabilizers and singular affine ambient space.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- A nonempty connected bounded semialgebraic subset relatively open in a complex affine algebraic variety is smooth and biholomorphic to a bounded symmetric domain when a discrete biholomorphism group acts properly with compact quotient.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary companion manuscript, attribution, prior-work, and exact Lean-scope review for non-notifying local inclusion.
Read this published revision