| # 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) | | |