K-Stability for Fano Manifolds with Torus Action of Complexity One
Algebraic Geometry
2022-05-20 v3 Differential Geometry
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.
Keywords
Cite
@article{arxiv.1507.04442,
title = {K-Stability for Fano Manifolds with Torus Action of Complexity One},
author = {Nathan Ilten and Hendrik Süß},
journal= {arXiv preprint arXiv:1507.04442},
year = {2022}
}
Comments
Updated to match journal version