A simply connected solvable Lie group with a left-invariant complex structure is shown to be non-Stein, providing a counterexample to Hasegawa's 2010 conjecture.
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math.DG 2years
2026 2representative citing papers
Simply connected nilpotent Lie groups with left-invariant nilpotent complex structures are biholomorphic to C^n by polynomial maps, so their lattices act freely and cocompactly on C^n by holomorphic polynomial automorphisms.
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A solvmanifold with a left-invariant complex structure whose universal cover is not Stein
A simply connected solvable Lie group with a left-invariant complex structure is shown to be non-Stein, providing a counterexample to Hasegawa's 2010 conjecture.
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Holomorphic polynomial crystallographic actions of nilpotent groups
Simply connected nilpotent Lie groups with left-invariant nilpotent complex structures are biholomorphic to C^n by polynomial maps, so their lattices act freely and cocompactly on C^n by holomorphic polynomial automorphisms.