Six dimensional solvmanifolds with holomorphically trivial canonical bundle

2014/01/02 by Anna Fino, Fino, Anna, Antonio Otal +3 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · doi:10.48550/arxiv.1401.0512

openalex publication_date 2014/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We determine the 6-dimensional solvmanifolds admitting an invariant complex structure with holomorphically trivial canonical bundle. Such complex structures are classified up to isomorphism, and the existence of strong Kähler with torsion (SKT), generalized Gauduchon, balanced and strongly Gauduchon metrics is studied. As an application we construct a holomorphic family (M,J_a) of compact complex manifolds such that (M,J_a) satisfies the ∂∂-Lemma and admits a balanced metric for any a\not=0, but the central limit neither satisfies the ∂∂-Lemma nor admits balanced metrics.

Citations

• Lattices, cohomology and models of six dimensional almost abelian\n solvmanifolds
• Complex structures on nilpotent Lie algebras

Cited by

• Kählerness of compact Hermitian surfaces under semi-definite Strominger-Bismut-Ricci curvatures

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• Six-dimensional complex solvmanifolds with non-invariant trivializing sections of their canonical bundle
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• SKT and Tamed Symplectic structures on solvmanifolds