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K-stability for Fano manifolds with torus action of complexity 1. (English) Zbl 1360.32020
Summary: We consider Fano manifolds admitting an algebraic torus action with general orbit of codimension \(1\). Using a recent result of Datar and Székelyhidi, 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 nontrivial Kähler-Ricci soliton.

MSC:
32Q20 Kähler-Einstein manifolds
14L30 Group actions on varieties or schemes (quotients)
14J45 Fano varieties
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