On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties

DOI10.1090/tran/8592zbMath1491.14059arXiv2108.02464OpenAlexW3189920897MaRDI QIDQ5863069

Camilla Felisetti, Qizheng Yin, Junliang Shen

Publication date: 10 March 2022

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.02464

zbMATH Keywords

Lagrangian fibrationHodge numbersperverse filtrationirreducible symplectic varietyperverse numbers

Mathematics Subject Classification ID

Fibrations, degenerations in algebraic geometry (14D06) Mixed Hodge theory of singular varieties (complex-analytic aspects) (32S35) Holomorphic symplectic varieties, hyper-Kähler varieties (14J42)

Related Items (1)

P=W conjectures for character varieties with symplectic resolution

Cites Work

• Unnamed Item
• Mapping class group and a global Torelli theorem for hyperkähler manifolds
• Topology of Hitchin systems and Hodge theory of character varieties: the case \(A_1\)
• Reflexive differential forms on singular spaces. Geometry and cohomology
• Differential forms on log canonical spaces
• Base manifolds for fibrations of projective irreducible symplectic manifolds
• Higgs bundles and local systems
• A Lie algebra attached to a projective variety
• Gopakumar-Vafa invariants via vanishing cycles
• A decomposition theorem for singular spaces with trivial canonical class of dimension at most five
• Lagrangian fibrations on symplectic fourfolds
• Cohomology of compact hyperkähler manifolds and its applications
• Topological mirror symmetry for rank two character varieties of surface groups
• Topology of Lagrangian fibrations and Hodge theory of hyper-Kähler manifolds
• Erratum to: ``Mapping class group and a global Torelli theorem for hyperkähler manifolds
• \(\mathrm{klt}\) varieties with trivial canonical class: holonomy, differential forms, and fundamental groups
• On base manifolds of Lagrangian fibrations
• Period mappings with applications to symplectic complex spaces
• Algebraic integrability of foliations with numerically trivial canonical bundle
• Action of the Lie algebra SO(5) on the cohomology of a hyperkähler manifold
• On the image of MRC fibrations of projective manifolds with semi-positive holomorphic sectional curvature
• Extension of 2-forms and symplectic varieties
• Examples of Irreducible Symplectic Varieties
• The Hodge theory of algebraic maps
• Symplectic singularities from the Poisson point of view
• The Hodge filtration on nonabelian cohomology
• A decomposition theorem for smoothable varieties with trivial canonical class
• The Hard Lefschetz Theorem and the topology of semismall maps
• Generators for the cohomology ring of the moduli space of rank 2 Higgs bundles
• P = W for Lagrangian fibrations and degenerations of hyper-Kähler manifolds
• Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities
• Low degree Hodge theory for klt varieties
• Singular spaces with trivial canonical class
• Semistability of the tangent sheaf of singular varieties
• Hitchin fibrations, abelian surfaces, and the P=W conjecture

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