K-Stability for Varieties with Torus Action

Nathan Ilten, Hendrik Süß

Published 2015-07-16Version 1

We consider Fano manifolds admitting an algebraic torus action with general orbit of codimension one. Using a recent result of Datar and Sz\'ekelyhidi, we effectively determine the existence of K\"ahler-Ricci solitons for those manifolds via the notion of equivariant K-stability. This allows us to give new examples of K\"ahler-Einstein Fano threefolds, and Fano threefolds admitting a non-trivial K\"ahler-Ricci soliton.