Geometry of nilmanifolds with left‐invariant complex structure and deformations in the large

By Sonke Rollenske. 2009

81 citations recorded by the source corpus.

The relation between nilmanifolds with left‐invariant complex structure and iterated principal holomorphic torus bundles is clarified and we give criteria under which deformations in the large are again of such type. As an application we obtain a fairly complete picture in complex dimension 3.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/222a116297e403f74fd2c1799572ea946a6ce80d

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

A correction to “Tamed symplectic forms and strong Kähler with torsion metrics” (2012, background): “(1) Since by [35] on a 2-step nilpotent Lie algebra every complex structure is nilpotent, Theorem 1.”
The Cohomologies of the Iwasawa Manifold and of Its Small Deformations (2012, background): “Fino in [6, Theorem 2]; see the surveys [5] and [24] and also [22] for more results in this direction.”
A Superficial Working Guide to Deformations and Moduli (2011, methodology): “Clemens’ proof uses directly the Kuranishi equation, and a similar method was used by Sönke Rollenske in [123], [124] in order to consider the deformation theory of complex manifolds yielding left invariant complex structures on nilmanifolds.”
Invariant Complex Structures on 6-Nilmanifolds: Classification, Frölicher Spectral Sequence and Special Hermitian Metrics (2011, background): “By [26] we can restrict our attention to the level of the Lie algebra and then, in view of Table 1, the above Hodge numbers follow directly from the proof of Proposition 6.”
Balanced Hermitian geometry on 6-dimensional nilmanifolds (2011, methodology): “Conditions under which the natural inclusion ( ∗,∗(g∗), ∂̄) →֒ (A(M), ∂̄) induces an isomorphism H(M,J) ∼= H(g, J) in cohomology are investigated in [5, 6, 19].”
Bott–Chern cohomology of solvmanifolds (2012, background): “(We refer to [71, 54, 13, 3, 25, 22, 59, 62] for definitions and notation.”