Delta-invariants for Fano varieties with large automorphism groups
A Golota�- International Journal of Mathematics, 2020 - World Scientific
International Journal of Mathematics, 2020•World Scientific
For a variety X, a big ℚ-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,− KX) 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.
a G-invariant version of the δ-threshold. We prove that for a Fano variety (X,− KX) 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.
For a variety , a big -divisor and a closed connected subgroup we define a -invariant version of the -threshold. We prove that for a Fano variety and a connected subgroup this invariant characterizes -equivariant uniform -stability. We also use this invariant to investigate -equivariant -stability of some Fano varieties with large groups of symmetries, including spherical Fano varieties. We also consider the case of being a finite group.
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