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

by Nathan Owen Ilten, Hendrik Süß

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 Kahler-Ricci solitons for those manifolds via the notion of equivariant K-stability. This allows us to give new examples of Kahler-Einstein Fano threefolds, and Fano threefolds admitting a non-trivial Kahler-Ricci soliton.

Reference:

K-Stability for Fano Manifolds with Torus Action of Complexity 1 (Nathan Owen Ilten, Hendrik Süß), Duke Mathematical Journal, volume 166, 2017.

Bibtex Entry:

@article{is17, author = {{Ilten}, Nathan Owen and S{\"u}{\ss}, Hendrik}, title = "{K-Stability for Fano Manifolds with Torus Action of Complexity 1}", journal = {Duke Mathematical Journal}, archivePrefix = "arXiv", eprint = {1507.04442}, primaryClass = "math.AG", keywords = {Mathematics - Algebraic Geometry, Mathematics - Differential Geometry, 32Q20, 14L30, 14J45}, year = 2017, pages = {177-204}, volume = 166, issue = 1, gsid={1558861318587888632,5881870906665656935}, doi={10.1215/00127094-3714864}, url={http://arxiv.org/abs/1507.04442}, 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 Kahler-Ricci solitons for those manifolds via the notion of equivariant K-stability. This allows us to give new examples of Kahler-Einstein Fano threefolds, and Fano threefolds admitting a non-trivial Kahler-Ricci soliton. }, }

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