• Corpus ID: 15635143

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

  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},
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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Algebraic geometry
  • R. Hartshorne
  • Mathematics, Computer Science
    Graduate texts in mathematics
  • 1977
It’s better to think of Algebraic Geometry as indicating a sub-area of mathematics as a whole, rather than a very precisely defined subfield.