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

Stefan Kebekus; Sandor J. Kovacs

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arXiv · 0707.2054

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

Stefan Kebekus·Sandor J. Kovacs

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Abstract

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 result, we can describe the fibration induced by the moduli map quite explicitly. A refined affirmative answer to Viehweg's conjecture for families over surfaces follows as a corollary.

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BibTeX RIS

Stefan Kebekus, Sandor J. Kovacs. 2007-07-13. The structure of surfaces mapping to the moduli stack of canonically polarized varieties. https://arxiv.org/abs/0707.2054

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