5 papers
Teichmüller and moduli spaces for complex nilmanifolds
Konstantin Wehler
We develop several tools to study the local and global structure of the Teichmüller and moduli spaces for complex nilmanifolds. As a starting point, we prove a structure theorem fo…
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…
Cohomology of CR structures on compact Lie groups
Howard Jacobowitz, Max Reinhold Jahnke, Vinícius Novelli +1
We show that, under a division condition, the tangential Cauchy--Riemann cohomology of a compact Lie group with a left-invariant CR structure can be computed on a suitable maximal…
Almost abelian complex nilmanifolds
Adrián Andrada, Romina M. Arroyo, María 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…
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…