Deformation of 2‐Step Nilmanifolds with Abelian Complex Structures
By C. Maclaughlin, H. Pedersen, Yat Sun Poon, S. Salamon. 2004
50 citations recorded by the source corpus.
We develop deformation theory for abelian invariant complex structures on a nilmanifold, and prove that in this case the invariance property is preserved by the Kuranishi process. A purely algebraic condition characterizes the deformations leading again to abelian structures, and we prove that such deformations are unobstructed. Various examples illustrate the resulting theory, and the behavior possible in three complex dimensions.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/6704c3e7cbf9b5b36af5657ae11e61b885705031
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In Applied Mathematics
- R. Villacampa
- Sonke Rollenske
- L. Ugarte
- A. Otal
- Manuel Ceballos
- M. L. Barberis
- Misha Verbitsky
- I. Dotti
In Geometry and Topology
- R. Villacampa
- Sonke Rollenske
- L. Ugarte
- A. Otal
- Manuel Ceballos
- M. L. Barberis
- Misha Verbitsky
- I. Dotti
Citations in the corpus
- Canonical bundles of complex nilmanifolds, with applications to hypercomplex geometry (2007, methodology): “Still, the vast empirical evidence (see e.g. [ MPPS ], [Po]) shows that some ana-”
- Hermitian structures on six-dimensional nilmanifolds (2004, background): “11 The deformation of abelian invariant complex structures on 2-step nilmanifolds is studied in [19], where it is proved that the Kuranishi process preserves the invariance of the deformed complex structures, at least for small deformations.”
- Geometry of nilmanifolds with left‐invariant complex structure and deformations in the large (2009, background): “Generalising results on deformations of abelian complex structures [8, 21] we proved the following theorem.”
- Invariant Complex Structures on 6-Nilmanifolds: Classification, Frölicher Spectral Sequence and Special Hermitian Metrics (2011, methodology): “Using the Kuranishi’s method, Maclaughlin, Pedersen, Poon and Salamon proved in [20] that J0 has a locally complete family of deformations consisting entirely of invariant complex structures and obtained the deformation parameter space in terms of invariant forms.”