Smooth projective varieties with a torus action of complexity 1 and Picard number 2

• Anne Fahrner ^[1] ; Jürgen Hausen ^[1] ; Michele Nicolussi ^[1]
  1. [1] Universität Tübingen, Germany
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 18, Nº 2, 2018, págs. 611-651
• Idioma: inglés
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• Resumen

  • We give an explicit description of all smooth varieties with a torus action of complexity one having Picard number at most two. As a consequence, we classify in every dimension the smooth (almost) Fano varieties with a torus action of complexity one having Picard number two. It turns out that all the Fano examples are obtained via an iterated generalized cone construction from a series of smooth varieties of dimension at most seven.