Torus equivariant K-stability
  It is conjectured that to test the K-polystability of a polarised variety it is enough to consider test-configurations which are equivariant with respect to a torus in the automorphism group. We prove partial results towards this conjecture. We also show that it would give a new proof of the K-polystability of constant scalar curvature polarised manifolds. 
Giulio Codogni, Jacopo Stoppa
math.AG math.DG