K-Stability for Fano Manifolds with Torus Action of Complexity One

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Abstract

We consider Fano manifolds admitting an algebraic torus action with general orbit of codimension one. Using a recent result of Datar and Szekelyhidi, we effectively determine the existence of Kähler-Ricci solitons for those manifolds via the notion of equivariant K-stability. This allows us to give new examples of Kähler-Einstein Fano threefolds, and Fano threefolds admitting a non-trivial Kähler-Ricci soliton.

Bibliographical metadata

Original languageEnglish
Pages (from-to)177-204
JournalDuke Mathematical Journal
Volume166
Issue number1
Early online date26 Oct 2016
DOIs
StatePublished - 1 Jan 2017