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

Abstract

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.

31 pages, new results added

References in corpus (1)

• An algorithm for the classification of smooth Fano polytopes

Cited by in corpus (4)

• On torus actions of higher complexity
• On smooth Fano fourfolds of Picard number two
• On intrinsic quadrics
• Classifying Fano Complexity-One $T$-Varieties via Divisorial Polytopes