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cfa2fd2 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | # Semialgebraic universal covers and bounded domains
The following describes the scope of the Lean formalization related to the following accompanying paper(s):
- [Symmetry of semialgebraic bounded domains with compact quotient](../../preprints/Symmetry-of-semialgebraic-bounded-domains-with-compact-quotient-September-24-2026/paper.pdf)
## Scope
The formalized result answers the paper's symmetry question affirmatively. A nonempty connected bounded semialgebraic subset, relatively open in a complex affine algebraic set, is smooth and biholomorphic to a bounded symmetric domain whenever a discrete group acts properly and holomorphically with compact quotient.
The action need not be free, and the ambient algebraic set may be singular.
## Comparator links
| Result | Comparator statement |
| --- | --- |
| Symmetry of semialgebraic bounded domains | [SymmetricDomains.lean](../ComparatorChallenges/SymmetricDomains.lean) |
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