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math.DG2026
Biholomorphism type of left-invariant complex structures on nilpotent Lie groups
Keizo Hasegawa, Sönke Rollenske, Lorenzo Sillari +2
In this note we prove a conjecture by Hasegawa stating that a simply connected, nilpotent Lie group of dimension endowed with a left-invariant complex structure is biholomorph…
math.DG2025
Almost abelian complex nilmanifolds
Adrián Andrada, Romina M. Arroyo, MarÃa L. Barberis +2
We show that a complex structure on a nilpotent almost abelian real Lie algebra is unique if it exists. As a consequence, we get full control over the cohomology and deformations o…
math.DG2024
Verbal ideals and unobstructed complex parallelisable nilmanifolds
Matthias Paulsen, Sönke Rollenske, Konstantin Wehler
We show that a compact complex parallelisable nilmanifold has unobstructed deformations if and only if its associated Lie algebra satisfies a reality condition and is a free Lie al…