K-stability of log del Pezzo hypersurfaces with index 2

Abstract

We completely classify K-stability of log del Pezzo hypersurfaces with index 2.

Unstable singular del Pezzo hypersurfaces with lower index

“…Then for any effective anticanonical Q-divisor H with Supp(H) ⊂ Supp(D), the log pair (S, H) is not log canonical at the base point. §3 K-stability K-stability for quasi-smooth well-formed del Pezzo hypersurfaces in three-dimensional weighted projective spaces with low indices is completely known by [2,5,7,8,13,17]. Indeed, Johnson and Kollár proved the existence of the Kähler-Einstein metric for almost cases of index I = 1 using α-invariant and Tian's criterion.…”

“…In particular, the exact values of global log canonical thresholds of infinite series are computed in [7]. In addition, the K-stability of indices, I = 2, 3 is determined in [5,17,18] by considering δ-invariants that was introduced by Fujita and Odaka in Fano varieties.…”

“…35 are 1 which implies (iv). In addition, for indices I = 2, 3, see [4,7,11] and the δ-invariants are computed in [5,17].…”

“…§5 Appendix Complete list of infinite series in [25] are presented in Table 1. K-stability of infinite series known so far along with the results in [2,4,5,7,8,11,13,17] is presented in Table 2.…”