Quadric cones on the boundary of the Mori cone for very general blowups of the plane

• Ciliberto, Ciro ^[1] ; Miranda, Rick ^[2] ; Roé, Joaquim ^[3]
  1. [1] University of Rome Tor Vergata

     University of Rome Tor Vergata

     Roma Capitale, Italia

     
  2. [2] Colorado State University

     Colorado State University

     Estados Unidos

     
  3. [3] Universitat Autònoma de Barcelona

     Universitat Autònoma de Barcelona

     Barcelona, España

     

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• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 76, Fasc. 3, 2025, págs. 601-611
• Idioma: inglés
• DOI: 10.1007/s13348-024-00447-7
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper we show the existence of cones over a 8-dimensional rational sphere at the boundary of the Mori cone of the blow-up of the plane at s\ge 13 very general points. This gives evidence for De Fernex’s strong \Delta-conjecture, which is known to imply Nagata’s conjecture. This also implies the existence of a multitude of good and wonderful rays as defined in Ciliberto et al. (Clay Math Proc 18:185–203, 2013).

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