OpenAI reports symmetry of semialgebraic bounded domains with compact quotient

Every nonempty connected bounded semialgebraic subset that is open in a complex affine algebraic variety is smooth and biholomorphic to a bounded symmetric domain if a discrete group of biholomorphisms acts properly with compact quotient.

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Understanding the problem

Read the background

Every nonempty connected bounded semialgebraic subset that is open in a complex affine algebraic variety is smooth and biholomorphic to a bounded symmetric domain if a discrete group of biholomorphisms acts properly with compact quotient.

Why it matters

If correct, answers the bounded-domain symmetry question of Kollár and Pardon.

What counts as progress

Must a bounded semialgebraic affine domain with a compact quotient be a bounded symmetric domain?

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