The Kollar-Pardon conjecture on projective varieties with semialgebraic universal cover

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Kollar and Pardon, Algebraic varieties with semialgebraic universal cover, J. Topology 5 (2012) evidence for this event

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Lean Comparator challenge SymmetricDomains (companion theorem only) evidence for this event

The Kollar-Pardon conjecture on projective varieties with semialgebraic universal cover parent of this event

Theorem 1.1: for a connected normal projective complex variety $X$, $\widetilde X$ is biholomorphic to a semialgebraic open subset of a projective variety if and only if $\widetilde X\cong D\times\mathbb C^m\times F$ with $D$ bounded symmetric and $F$ simply connected normal projective (either may be a point); no algebraicity of deck transformations is assumed and the compact factor may be singular. The cover is quasi-projective exactly when $D$ is a point; a smooth projective variety covered by $\mathbb C^n$ is finitely etale covered by an abelian variety. The companion proves that a connected bounded semialgebraic open subset of an affine variety with a proper cocompact holomorphic group action is smooth and a bounded symmetric domain. Not covered: non-normal or non-projective (e.g. compact Kahler) $X$. parent of this event

VibeMathed record: The Kollar-Pardon conjecture on projective varieties with semialgebraic universal cover evidence for this event

Companion: Symmetry of semialgebraic bounded domains with compact quotient (answers Kollar-Pardon Question 25) evidence for this event

The Kollar-Pardon conjecture on projective varieties with semialgebraic universal cover evidence for this event

Lean solution module OAI/Analysis/SymmetricDomains/Main.lean evidence for this event