76 citations · 216 across the 33 of their papers we have counts for
7 papers · 1 filter
Yet Another Family of Complex Structures on
Wenfei Liu, Sönke Rollenske
Following a similar path as the recent construction of a complex structure on we construct another such family, disjoint from the known ones.
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…
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…
Dolbeault cohomology of complex nilmanifolds foliated in toroidal groups
Anna Fino, Sönke Rollenske, Jean Ruppenthal
It is conjectured that the Dolbeault cohomology of a complex nilmanifold is computed by left-invariant forms. We prove this under the assumption that is suitably foliated i…
Dolbeault cohomology of nilmanifolds with left-invariant complex structure
Sönke Rollenske
We discuss the known evidence for the conjecture that the Dolbeault cohomology of nilmanifolds with left-invariant complex structure can be computed as Lie-algebra cohomology and a…