Work

∂ ∂ ¯ -lemma and Bott–Chern cohomology of twistor spaces

Year: 2026

Type: article

Abstract: In the paper we study the Bott-Chern and Aeppli cohomologies of the twistor space of a compact self-dual 4-manifold and we characterize the validity of the ∂ ∂ ¯ -lemma. We also compute explicitly the Dolbeault cohomology of the twistor space Z of the flat 4-dimensional torus, which is known to not satisfy the ∂ ∂ ¯ lemma.

Source: Expositiones Mathematicae

DOI: 10.1016/j.exmath.2026.125755

Authors: Anna Fino, Gueo Grantcharov, Nicoletta Tardini, Adriano Tomassini, Luigi Vezzoni

Institutions: Florida International University, University of Turin, Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, University of Parma

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,500

Funders: Simons Foundation, American Institute of Mathematics, Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni