Base Spaces of Non-Isotrivial Families of Smooth Minimal Models

By E. Viehweg, K. Zuo. 2001

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Given a polynomial h of degree n let M h be the moduli functor of canonically polarized complex manifolds with Hilbert polynomial h. By [23] there exist a quasi-projective scheme M h together with a natural transformation $$ \Psi :\mathcal{M}_h \to Hom(\_,M_h ) $$ such that M h is a coarse moduli scheme for M h . For a complex quasi-projective manifold U we will say that a morphism ϕ U → M h factors through the moduli stack, or that ϕ is induced by a family, if ϕ lies in the image of Ψ(U), hence if ϕ = Ψ(ƒ: V → U).

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b6a4a95334b6b8d62280356a83154a9e82e9b224

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Citations in the corpus

Families of canonically polarized varieties over surfaces (2005, background): “Families over a curve have been studied by several authors in recent years and they are now fairly well understood—the strongest results known were obtained in [20,21], and [14].”
COMPLEX MULTIPLICATION, GRIFFITHS-YUKAWA COUPLINGS, AND RIGIDITY FOR FAMILIES OF HYPERSURFACES (2003, methodology): “To be more precise, let Y be a projective manifold and S ⊂ Y the complement of a normal crossing divisor . Assume that for so me (d, n) and for all generically finite morphisms S → Md,n, factoring through the moduli stack, the sheaf 1Y (log) is big (see [ 22 ], Definition 1.1).”