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15 January 2017 K-stability for Fano manifolds with torus action of complexity 1
Nathan Ilten, Hendrik Süß
Duke Math. J. 166(1): 177-204 (15 January 2017). DOI: 10.1215/00127094-3714864

Abstract

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.

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Nathan Ilten. Hendrik Süß. "K-stability for Fano manifolds with torus action of complexity 1." Duke Math. J. 166 (1) 177 - 204, 15 January 2017. https://doi.org/10.1215/00127094-3714864

Information

Received: 28 July 2015; Revised: 4 March 2016; Published: 15 January 2017
First available in Project Euclid: 26 October 2016

zbMATH: 1360.32020
MathSciNet: MR3592691
Digital Object Identifier: 10.1215/00127094-3714864

Subjects:
Primary: 32Q20
Secondary: 14J45, 14L30

Rights: Copyright © 2017 Duke University Press

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Vol.166 • No. 1 • 15 January 2017
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