The isotriviality of smooth families of canonically polarized manifolds over a special quasi-projective base

DOI10.1112/S0010437X1600734XzbMath1427.14031arXiv1310.5391MaRDI QIDQ2816795

Behrouz Taji

Publication date: 25 August 2016

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.5391

zbMATH Keywords

Kodaira dimensionminimal model programfamiliesmodulispecial varietiesisotriviality

Mathematics Subject Classification ID

Algebraic moduli of abelian varieties, classification (14K10) Families, moduli, classification: algebraic theory (14J10) Minimal model program (Mori theory, extremal rays) (14E30) Subvarieties of abelian varieties (14K12) Fine and coarse moduli spaces (14D22) Stacks and moduli problems (14D23)

Related Items (12)

Algebraicity of foliations on complex projective manifolds, applications ⋮ Specialness and isotriviality for regular algebraic foliations ⋮ Foliations with positive slopes and birational stability of orbifold cotangent bundles ⋮ Isotriviality of smooth families of varieties of general type ⋮ Birational geometry of smooth families of varieties admitting good minimal models ⋮ Chern class inequalities for nonuniruled projective varieties ⋮ Logarithmic Kodaira dimension and zeros of holomorphic log-one-forms ⋮ Hyperbolicity of singular spaces ⋮ Néron models and the arithmetic Shafarevich conjecture for certain canonically polarized surfaces ⋮ On the Kodaira dimension of base spaces of families of manifolds ⋮ Orbifold generic semi-positivity: an application to families of canonically polarized manifolds ⋮ Viehweg's hyperbolicity conjecture for families with maximal variation

Cites Work

• Positive sheaves of differentials coming from coarse moduli spaces
• The structure of surfaces and threefolds mapping to the moduli stack of canonically polarized varieties
• Families over special base manifolds and a conjecture of Campana
• Orbifold generic semi-positivity: an application to families of canonically polarized manifolds
• Orbifolds, special varieties and classification theory.
• Orbifoldes géométriques spéciales et classification biméromorphe des variétés kählériennes compactes
• Existence of minimal models for varieties of log general type
• The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension
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