Families of varieties of general type over compact bases

• Autores: Stefan Kebekus, Sándor J. Kovács
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 218, Nº 3, 2008, págs. 649-652
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.01.005
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• Resumen

  • Let be a smooth family of canonically polarized complex varieties over a smooth base. Generalizing the classical Shafarevich hyperbolicity conjecture, Viehweg conjectured that Y is necessarily of log general type if the family has maximal variation. A somewhat stronger and more precise version of Viehweg's conjecture was shown by the authors in [S. Kebekus, S.J. Kovács, Families of canonically polarized varieties over surfaces, preprint math.AG/0511378; Invent. Math. (2008), doi: 10.1007/s00222-008-0128-8; S. Kebekus, S.J. Kovács, The structure of surfaces mapping to the moduli stack of canonically polarized varieties, arXiv: 0707.2054v1 [math.AG], 2007] in the case where Y is a quasi-projective surface. Assuming that the minimal model program holds, this very short paper proves the same result for projective base manifolds Y of arbitrary dimension