The LLV decomposition of hyperkähler cohomology and applications to the Nagai conjecture (after Green-Kim-Laza-Robles)

DOI10.1007/s00032-022-00362-1OpenAlexW4296186079WikidataQ123151596 ScholiaQ123151596MaRDI QIDQ2107599

Jieao Song, Georg Oberdieck

Publication date: 2 December 2022

Published in: Milan Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00032-022-00362-1

Mathematics Subject Classification ID

Hyper-Kähler and quaternionic Kähler geometry, ``special geometry (53C26) Holomorphic symplectic varieties, hyper-Kähler varieties (14J42)

Cites Work

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• Perverse sheaves and the cohomology of Hilbert schemes of smooth algebraic surfaces
• Heisenberg algebra and Hilbert schemes of points on projective surfaces
• A Lie algebra attached to a projective variety
• The Douady space of a complex surface
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• On the cohomology ring of a simple hyperkähler manifold (on the results of Verbitsky)
• Motivic decompositions for the Hilbert scheme of points of a \(K3\) surface
• A Lie algebra action on the Chow ring of the Hilbert scheme of points of a \(K3\) surface
• The Looijenga-Lunts-Verbitsky algebra and Verbitsky's theorem
• On the Hodge and Betti numbers of hyper-Kähler manifolds
• The LLV decomposition of hyper-Kähler cohomology (the known cases and the general conjectural behavior)
• On monodromies of a degeneration of irreducible symplectic Kähler manifolds
• Limit mixed Hodge structures of hyperk\"ahler manifolds

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