On manifolds swept out by high dimensional hypersurfaces

• Taku Suzuki ^[1]
  1. [1] Waseda University

     Waseda University

     Japón

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 12 (December 2015), 2015, págs. 5394-5401
• Idioma: inglés
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• Resumen

  • In this paper, we prove that, if an embedded smooth projective manifold is swept out by high dimensional hypersurfaces of degree d, then either it is a scroll, or it admits an extremal contraction whose general fibers are hypersurfaces of degree d, under the assumption of Hartshorne's famous conjecture on complete intersections.