Remarks on Dolbeault cohomology of Oeljeklaus-Toma manifolds and Hodge theory
Hisashi Kasuya
TL;DR
This paper explicitly constructs harmonic representatives for Dolbeault and Bott-Chern cohomologies of Oeljeklaus-Toma manifolds, demonstrating their geometric Dolbeault formality and analyzing related inequalities.
Contribution
It provides explicit harmonic representatives for cohomologies of Oeljeklaus-Toma manifolds and explores their geometric and cohomological properties.
Findings
Harmonic representatives explicitly constructed for Dolbeault cohomology.
Demonstration of geometric Dolbeault formality.
Analysis of Angella-Tomassini inequality for these manifolds.
Abstract
We give explicit harmonic representatives of Dolbeault cohomology of Oeljeklaus-Toma manifolds and show that they are geometrically Dolbeault formal. We also give explicit harmonic representatives of Bott-Chern cohomology of Oeljeklaus-Toma manifolds of type and study the Angella-Tomassini inequality.
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Taxonomy
TopicsGeometry and complex manifolds · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory