Duke Mathematical Journal

K-stability for Fano manifolds with torus action of complexity 1

Nathan Ilten and Hendrik Süß

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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.

Article information

Duke Math. J., Volume 166, Number 1 (2017), 177-204.

Received: 28 July 2015
Revised: 4 March 2016
First available in Project Euclid: 26 October 2016

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Zentralblatt MATH identifier

Primary: 32Q20: Kähler-Einstein manifolds [See also 53Cxx]
Secondary: 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] 14J45: Fano varieties

K-stability Kähler–Einstein metric $T$-varieties torus action Fano varieties


Ilten, Nathan; Süß, Hendrik. K-stability for Fano manifolds with torus action of complexity $1$. Duke Math. J. 166 (2017), no. 1, 177--204. doi:10.1215/00127094-3714864. https://projecteuclid.org/euclid.dmj/1477494164

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