Remark: Family 058. The Kollár–Pardon universal-cover conjecture

Proves the Kollár–Pardon conjecture: the semialgebraic universal covers of connected normal projective complex varieties are exactly products $D\times {\mathbb{C}}^m\times F$, with $D$ bounded symmetric and $F$ simply connected, normal, and projective. A universal cover is quasi-projective exactly when the bounded symmetric factor is absent. In particular, a smooth projective variety covered by ${\mathbb{C}}^n$ has a finite étale cover by an abelian variety.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.