Hodge theory of degenerations. I: Consequences of the decomposition theorem
From MaRDI portal
Publication:2047270
DOI10.1007/s00029-021-00675-wzbMath1478.14024arXiv1901.01896OpenAlexW3191163561MaRDI QIDQ2047270
Morihiko Saito, Radu Laza, Matthew Kerr
Publication date: 19 August 2021
Published in: Selecta Mathematica. New Series (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1901.01896
Fibrations, degenerations in algebraic geometry (14D06) Variation of Hodge structures (algebro-geometric aspects) (14D07)
Related Items (5)
Moduli space holography and the finiteness of flux vacua ⋮ Remarks on eigenspectra of isolated singularities ⋮ Unimodal singularities and boundary divisors in the KSBA moduli of a class of Horikawa surfaces ⋮ Apéry extensions ⋮ Deformations of varieties of general type
Cites Work
- The KSBA compactification for the moduli space of degree two \(K3\) pairs
- Modules de Hodge polarisables. (Polarisable Hodge modules)
- Insignificant limit singularities of surfaces and their mixed Hodge structure
- Perverse obstructions to flat regular compactifications
- Log-plurigenera in stable families of surfaces
- Sur le théorème local des cycles invariants. (On the local invariant cycle theorem)
- Hodge filtrations on Gauss-Manin systems. II
- Singularities of admissible normal functions (with an appendix by Najmuddin Fakhruddin)
- Decomposition theorem for proper Kähler morphisms
- The perverse filtration and the Lefschetz hyperplane theorem
- The moduli space of cubic fourfolds via the period map
- \(L^ 2\) and intersection cohomologies for a polarizable variation of Hodge structure
- Théorème de Torelli pour les cubiques de \({\mathbb{P}}^ 5\). (Torelli theorem for the cubics of \({\mathbb{P}}^ 5)\)
- The Poincaré lemma for variations of polarized Hodge structure
- Threefolds and deformations of surface singularities
- Limits of Hodge structures
- La fonction zeta d'une monodromie
- Degeneration of Kähler manifolds
- A complete moduli space for K3 surfaces of degree 2
- On \(b\)-function, spectrum and rational singularity
- Algebraic geometry. III. Complex algebraic varieties, algebraic curves and their Jacobians. Transl. from the Russian by I. Rivin
- Compactifications defined by arrangements. II: Locally symmetric varieties of type IV
- A hyper-Kähler compactification of the intermediate Jacobian fibration associated with a cubic 4-fold
- The Leray spectral sequence is motivic
- Weak semistable reduction in characteristic 0
- GIT versus Baily-Borel compactification for \(K3\)'s which are double covers of \(\mathbb{P}^1 \times \mathbb{P}^1\)
- Semistable reduction in characteristic 0
- Polarized relations on horizontal \(\operatorname{SL}(2)\)'s
- GIT versus Baily-Borel compactification for quartic \(K3\) surfaces
- Specialization of cycles and the \(K \)-theory elevator
- Théoreme de Lefschetz et critères de dégénérescence de suites spectrales
- Equations différentielles à points singuliers réguliers
- Comparison of de Rham and Dolbeault cohomology for proper surjective mappings
- Some remarks on limit mixed Hodge structure and spectrum
- Decomposition theorem for semi-simples
- The moduli space of cubic threefolds as a ball quotient
- An Exponential History of Functions with Logarithmic Growth
- The Hodge theory of algebraic maps
- Log canonical singularities are Du Bois
- A Simple Characterization of Du Bois Singularities
- Hodge-theoretic aspects of the Decomposition Theorem
- Degenerations of K3 Surfaces of Degree 4
- Geometric Invariant Theory
- Introduction
- Local stable reduction of plane curve singularities
- Complete moduli of cubic threefolds and their intermediate Jacobians
- Birational geometry of the moduli space of quartic surfaces
- Vanishing cycle sheaves of one-parameter smoothings and quasi-semistable degenerations
- Mixed Hodge Structures
- Singular Points of Complex Hypersurfaces. (AM-61)
- Mixed Hodge modules
- Unit interval orders and the dot action on the cohomology of regular semisimple Hessenberg varieties
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Hodge theory of degenerations. I: Consequences of the decomposition theorem
