K-Stability for Fano Manifolds with Torus Action of Complexity 1

Nathan Owen Ilten, Hendrik Süß

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

    Keywords

    • K-stability
    • Kahler-Einstein metric
    • T-variety
    • torus action
    • Fano variety

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