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Regular version of the site

Article

Delta-invariants for Fano varieties with large automorphism groups

International Journal of Mathematics. 2020. Vol. 31. No. 10. P. 2050077.

For a variety 𝑋, a big -divisor 𝐿 and a closed connected subgroup 𝐺⊂Aut(𝑋,𝐿) we define a 𝐺-invariant version of the 𝛿-threshold. We prove that for a Fano variety (𝑋,−𝐾_𝑋) and a connected subgroup 𝐺⊂Aut(𝑋) this invariant characterizes 𝐺-equivariant uniform 𝐾-stability. We also use this invariant to investigate 𝐺-equivariant 𝐾-stability of some Fano varieties with large groups of symmetries, including spherical Fano varieties. We also consider the case of 𝐺 being a finite group.