Compactifications of smooth families and of moduli spaces of polarized manifolds

  title={Compactifications of smooth families and of moduli spaces of polarized manifolds},
  author={Eckart Viehweg},
  journal={Annals of Mathematics},
  • E. Viehweg
  • Published 3 May 2006
  • Mathematics
  • Annals of Mathematics
Let M h be the moduli scheme of canonically polarized manifolds with Hilbert polynomial h. We construct for v ≥ 2 with h(v) > 0 a projective compactification M h of the reduced moduli scheme (M h ) red such that the ample invertible sheaf λ ν , corresponding to det( f * ω v X0/Y0 ) on the moduli stack, has a natural extension λ ν ∈ Pic(M h ) ℚ . A similar result is shown for moduli of polarized minimal models of Kodaira dimension zero. In both cases "natural" means that the pullback of λ ν to a… 
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