Threefolds with quasi-projective universal cover
Beno\^it Claudon (IECN), Andreas Hoering (IMJ)

TL;DR
This paper investigates compact Kähler threefolds with infinite fundamental groups whose universal covers can be compactified, revealing that such conditions strongly restrict the geometry, leading to a product structure involving affine space.
Contribution
It demonstrates that projective threefolds with infinite fundamental groups and quasi-projective universal covers are isomorphic to a product of an affine space with a simply connected manifold.
Findings
Universal cover can be expressed as a product involving affine space.
Strong restrictions on the geometry of threefolds with such universal covers.
Conditions imply the universal cover is quasi-projective and has a specific product structure.
Abstract
We study compact K\"ahler threefolds X with infinite fundamental group whose universal cover can be compactified. Combining techniques from -theory, Campana's geometric orbifolds and the minimal model program we show that this condition imposes strong restrictions on the geometry of X. In particular we prove that if a projective threefold with infinite fundamental group has a quasi-projective universal cover, the latter is then isomorphic to the product of an affine space with a simply connected manifold.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Geometric Analysis and Curvature Flows
