Cohomology of holomorphic line bundles and Hodge symmetry on Oeljeklaus-Toma manifolds
Hisashi Kasuya
TL;DR
This paper investigates the Dolbeault cohomology of Oeljeklaus-Toma manifolds with holomorphic line bundles, establishing Hodge symmetry and identifying conditions for cohomology vanishing and non-vanishing.
Contribution
It proves Hodge symmetry for Dolbeault cohomology with line bundle coefficients and characterizes cohomology vanishing on Oeljeklaus-Toma manifolds.
Findings
Hodge symmetry holds for Dolbeault cohomology with line bundle values
Vanishing and non-vanishing results for Dolbeault cohomology are established
Results deepen understanding of complex geometry on Oeljeklaus-Toma manifolds
Abstract
We prove the Hodge symmetry type result on the Dolbeault cohomology of Oeljeklaus-Toma manifolds with values in the direct sum of holomorphic line bundles. Consequently, we show the vanishing and non-vanishing of Dolbeault cohomology of Oeljeklaus-Toma manifolds with values in holomorphic line bundles.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology