TL;DR
The paper introduces the perverse-Hodge octahedron, a 3D structure extending the Hodge diamond of hyperkähler manifolds, linked to Nagai's conjecture and related work.
Contribution
It defines the perverse-Hodge octahedron and shows its equivalence to Nagai's conjecture, connecting it to existing geometric structures.
Findings
The octahedron exists for all known deformation types.
It is implicitly present in prior work by Huybrechts-Mauri and Shen-Yin.
The structure provides new insights into hyperkähler geometry.
Abstract
The perverse-Hodge octahedron is a 3D enhancement of the Hodge diamond of a compact hyperk\"{a}hler manifold. Its existence is equivalent to Nagai's conjecture, which holds for all known deformation types. The octahedron appears implicitly in Huybrechts-Mauri and Shen-Yin.
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Taxonomy
TopicsMathematics and Applications