Minimal Model of a Nilmanifold and Moduli Space of Complex Structures

D. V. Millionshchikov

Informatics and Automation, Geometry, Topology, and Mathematical Physics, Tome 325 (2024), pp. 201-231

Résumé

For an arbitrary real nilpotent Lie algebra (nilmanifold) with an integrable complex structure, we propose an algorithm for constructing a special model of this nilmanifold that includes information on the complex structure. As a main application, we obtain a classification of eight-dimensional $2$-generated nilpotent Lie algebras that admit an integrable complex structure. We also describe the moduli spaces of complex structures for each Lie algebra from the resulting classification list.

Détail

Keywords: nilmanifold, nilpotent Lie algebra, complex structure, lower central series, minimal model, Dolbeault cohomology.

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