On the Kodaira dimension of orthogonal modular varieties

DOI10.1007/s00222-017-0781-xzbMath1428.14040arXiv1701.03225OpenAlexW2591399222MaRDI QIDQ1645327

Shouhei Ma

Publication date: 28 June 2018

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.03225

zbMATH Keywords

orthogonal groupKodaira dimensionintegral latticesmodular varietiesreflective modular forms

Mathematics Subject Classification ID

Algebraic moduli problems, moduli of vector bundles (14D20) Other groups and their modular and automorphic forms (several variables) (11F55) Modular and Shimura varieties (14G35) Moduli, classification: analytic theory; relations with modular forms (14J15)

Related Items (16)

Reflective modular forms on lattices of prime level ⋮ A global Torelli theorem for singular symplectic varieties ⋮ Examples of lattice-polarized K3 surfaces with automorphic discriminant, and Lorentzian Kac–Moody algebras ⋮ Special holomorphic tensors on orthogonal modular varieties and applications to the Lang conjecture ⋮ Uniruledness of some low-dimensional ball quotients ⋮ Irregular cusps of ball quotients ⋮ The perfect cone compactification of quotients of type IV domains ⋮ The classification of 2-reflective modular forms ⋮ Reflective obstructions of unitary modular varieties ⋮ Fano Shimura varieties with mostly branched cusps ⋮ Kodaira dimension of moduli of special \(K3^{[2}\)-fourfolds of degree 2] ⋮ $K3$ surfaces with involution and analytic torsion ⋮ The Kodaira dimension of some moduli spaces of elliptic K3 surfaces ⋮ Reflective automorphic forms on lattices of squarefree level ⋮ Reflective modular forms and applications ⋮ The classification of free algebras of orthogonal modular forms

Uses Software

• sfqm

Cites Work

• Moduli spaces of polarized symplectic O'Grady varieties and Borcherds products
• Abelianisation of orthogonal groups and the fundamental group of modular varieties
• Automorphic forms with singularities on Grassmannians
• Algebraic classification of linking pairings on 3-manifolds
• Hirzebruch's proportionality theorem in the non-compact case
• On the Kodaira dimension of the moduli space of Abelian varieties
• The Gross-Kohnen-Zagier theorem in higher dimensions
• Kodaira dimension of moduli of special cubic fourfolds
• The Hirzebruch-Mumford volume for the orthogonal group and applications
• The Kodaira dimension of the moduli of \(K3\) surfaces
• Hirzebruch-Mumford proportionality and locally symmetric varieties of orthogonal type
• On the classification of automorphic products and generalized Kac-Moody algebras
• Irreducible symplectic 4-folds and Eisenbud-Popescu-Walter sextics
• Automorphic products of singular weight for simple lattices
• Quadratic forms on finite groups, and related topics
• Lattices with many Borcherds products
• Rationality of the moduli spaces of 2-elementary 𝐾3 surfaces
• Moduli spaces of irreducible symplectic manifolds
• On the compactification of moduli spaces for algebraic 𝐾3 surfaces
• INTEGRAL SYMMETRIC BILINEAR FORMS AND SOME OF THEIR APPLICATIONS
• On a Relation Between ~ SL   2   Cusp Forms and Cusp Forms on Tube Domains Associated to Orthogonal Groups
• AUTOMORPHIC FORMS AND LORENTZIAN KAC–MOODY ALGEBRAS PART I
• Families of K3 surfaces
• Finiteness results for compact hyperkähler manifolds
• Automorphic products of singular weight
• Eisenstein series attached to lattices and modular forms on orthogonal groups
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