On the hyperbolicity of base spaces for maximally variational families of smooth projective varieties (with an appendix by Dan Abramovich)

DOI10.4171/JEMS/1152zbMath1487.32146OpenAlexW3213200924MaRDI QIDQ2135432

Yanyan Li

Publication date: 6 May 2022

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/jems/1152

zbMATH Keywords

moduli spacesBrody hyperbolicitypseudo Kobayashi hyperbolicity

Mathematics Subject Classification ID

Variation of Hodge structures (algebro-geometric aspects) (14D07) Hyperbolic and Kobayashi hyperbolic manifolds (32Q45) Birational geometry (14E99)

Cites Work

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• Kodaira dimension of algebraic fiber spaces over abelian varieties
• The structure of surfaces and threefolds mapping to the moduli stack of canonically polarized varieties
• Viehweg's hyperbolicity conjecture is true over compact bases
• On the hyperbolicity of general hypersurfaces
• Orbifold generic semi-positivity: an application to families of canonically polarized manifolds
• A criterion for flatness of Hodge bundles over curves and geometric applications
• Hyperbolicity of generic high-degree hypersurfaces in complex projective space
• Families of canonically polarized varieties over surfaces
• Bergman kernels and the pseudoeffectivity of relative canonical bundles
• The asymptotic behavior of a variation of polarized Hodge structure
• Chern forms and the Riemann tensor for the moduli space of curves
• Threefolds and deformations of surface singularities
• Number theory III: Diophantine geometry
• Variation of Hodge structure: The singularities of the period mapping
• On the Brody hyperbolicity of moduli spaces for canonically polarized manifolds.
• Positivity of relative canonical bundles and applications
• Augmented Weil-Petersson metrics on moduli spaces of polarized Ricci-flat Kähler manifolds and orbifolds
• Degeneration of Hodge structures
• Frobenius amplitude and strong vanishing theorems for vector bundles. With an appendix by Dennis S. Keeler.
• Weak semistable reduction in characteristic 0
• Kobayashi hyperbolicity of the complements of general hypersurfaces of high degree
• Finsler metrics and Kobayashi hyperbolicity of the moduli spaces of canonically polarized manifolds
• Brody hyperbolicity of base spaces of certain families of varieties
• Recent results on the Kobayashi and Green-Griffiths-Lang conjectures
• Stable maps in higher dimensions
• Fujita decomposition over higher dimensional base
• Viehweg's hyperbolicity conjecture for families with maximal variation
• Pseudo Kobayashi hyperbolicity of subvarieties of general type on abelian varieties
• Foliations with positive slopes and birational stability of orbifold cotangent bundles
• Families of varieties of general type over compact bases
• Weak positivity and the stability of certain Hilbert points. II
• Compactifying the space of stable maps
• Hyperbolicity, automorphic forms and Siegel modular varieties
• Moduli of products of stable varieties
• Stable varieties with a twist
• Positivity of twisted relative pluricanonical bundles and their direct images
• Minimal models and the Kodaira dimension of algebraic fiber spaces.
• ON COVERINGS OF DELIGNE–MUMFORD STACKS AND SURJECTIVITY OF THE BRAUER MAP
• Hyperbolicity of singular spaces
• On a theorem of Campana and P\u{a}un
• Moduli of canonically polarized manifolds, higher order Kodaira-Spencer maps, and an analogy to Calabi-Yau manifolds
• Albanese maps of projective manifolds with nef anticanonical bundles
• Projectivity of the moduli space of stable log-varieties and subadditivity of log-Kodaira dimension
• Positivity properties of the bundle of logarithmic tensors on compact Kähler manifolds
• On the negativity of kernels of Kodaira-Spencer maps on Hodge bundles and applications

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