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arXiv · 1602.04360

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

Anne Fahrner·Juergen Hausen·Michele Nicolussi
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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.

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Anne Fahrner, Juergen Hausen, Michele Nicolussi. 2016-02-13. Smooth projective varieties with a torus action of complexity 1 and Picard number 2. https://doi.org/10.2422/2036-2145.201608_024

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