• Corpus ID: 15635143

# The structure of surfaces mapping to the moduli stack of canonically polarized varieties

@article{Kebekus2007TheSO,
title={The structure of surfaces mapping to the moduli stack of canonically polarized varieties},
author={Stefan Kebekus and S{\'a}ndor Kov{\'a}cs},
journal={arXiv: Algebraic Geometry},
year={2007}
}
• Published 13 July 2007
• Mathematics
• arXiv: Algebraic Geometry
Generalizing the well-known Shafarevich hyperbolicity conjecture, it has been conjectured by Viehweg that a quasi-projective manifold that admits a generically finite morphism to the moduli stack of canonically polarized varieties is necessarily of log general type. Given a quasi-projective surface that maps to the moduli stack, we employ extension properties of logarithmic pluri-forms to establish a strong relationship between the moduli map and the minimal model program of the surface. As a…
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