P = W for Lagrangian fibrations and degenerations of hyper-Kähler manifolds

DOI10.1017/fms.2021.31zbMath1467.14101arXiv1908.07510OpenAlexW3134856905MaRDI QIDQ5004649

Junliang Shen, A. Harder, Qizheng Yin, Zhi-yuan Li

Publication date: 3 August 2021

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.07510

Mathematics Subject Classification ID

Fibrations, degenerations in algebraic geometry (14D06) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Holomorphic symplectic varieties, hyper-Kähler varieties (14J42)

Related Items

The LLV decomposition of hyper-Kähler cohomology (the known cases and the general conjectural behavior), P=W conjectures for character varieties with symplectic resolution, Deformations of compact Prym fibrations to Hitchin systems, Perverse filtrations, Chern filtrations, and refined BPS invariants for local \(\mathbb{P}^2\), Topology of Lagrangian fibrations and Hodge theory of hyper-Kähler manifolds, On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties, Hitchin fibrations, abelian surfaces, and the P=W conjecture, Lagrangian fibrations

Cites Work

• Topology of Hitchin systems and Hodge theory of character varieties: the case \(A_1\)
• Higgs bundles and local systems
• Limits of Hodge structures
• A Lie algebra attached to a projective variety
• Cohomology of compact hyperkähler manifolds and its applications
• Kuga-Satake construction and cohomology of hyperkähler manifolds
• Topology of Lagrangian fibrations and Hodge theory of hyper-Kähler manifolds
• On monodromies of a degeneration of irreducible symplectic Kähler manifolds
• Action of the Lie algebra SO(5) on the cohomology of a hyperkähler manifold
• The Weights of the Tautological Classes of Character Varieties
• Limit mixed Hodge structures of hyperk\"ahler manifolds
• Polarizations on limiting mixed Hodge structures