https://neckpinch.com/authors/minghao-miao/New arXiv papers by Minghao Miao, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2401.13999arxiv:2401.13999Thu, 25 Jan 2024 00:00:00 GMTMinghao Miao, Linsheng Wang — We explicitly determine the optimal degenerations of Fano threefolds X in family No 2.23 of Mori-Mukai's list as predicted by the Hamilton-Tian conjecture. More precisely, we find a special degeneration (𝓧, ξ₀) of X such that (𝓧₀, ξ₀) is weighted K-polystable, which is equivalent to (𝓧₀, ξ₀) admitting a Kähler-Ricci soliton (KRS) by and. Furthermore, we study the moduli spaces of (𝓧₀, ξ₀). The H-invariant of X divides the natural parameter space into two strata, which leads to different moduli spaces of KRS Fano varieties. We show that one of them is isomorphic to the GIT-moduli space of biconic curves C⊆ ℙ¹× ℙ¹, and the other one is a single point.Ricci solitonsKähler–Ricci solitons3-manifoldsKähler geometryStability & uniquenessKähler–Einstein & K-stability https://arxiv.org/abs/2309.14212arxiv:2309.14212Mon, 25 Sep 2023 00:00:00 GMTMinghao Miao, Linsheng Wang — We find Fano threefolds X admitting Kähler-Ricci solitons (KRS) with non-trivial moduli, which are T-varieties of complexity two. More precisely, we show that the weighted K-stability of (X,ξ₀) (where ξ₀ is the soliton candidate) is equivalent to certain GIT-stability. In particular, this provides the first examples of strictly weighted K-semistable Fano varieties. On the other hand, we generalize Koiso's theorem to the log Fano setting. Indeed, we show that the K-stability of a log Fano pair (V,Δ_V) is equivalent to the weighted K-stability of a cone (Y, Δ_Y, ξ₀) over it. This also leads to new examples of KRS Fano varieties with non-trivial moduli and small automorphism groups. To achieve these, we establish the weighted Abban-Zhuang estimate generalizing the work of, which gives a lower bound of the weighted stability threshold δ^g_T(X,Δ). This is an effective way to check the weighted K-semistablity of a log Fano triple (X,Δ,ξ₀). This estimate is also useful in testing (weighted) K-polystability based on the work of.Ricci solitonsKähler–Ricci solitons3-manifoldsKähler geometryStability & uniquenessKähler–Einstein & K-stability https://arxiv.org/abs/2210.15263arxiv:2210.15263Thu, 27 Oct 2022 00:00:00 GMTMinghao Miao, Gang Tian — In this note, we show that the solution of Kähler-Ricci flow on every Fano threefold from the family No.2.23 in the Mori-Mukai's list develops type II singularity. In fact, we show that no Fano threefold from the family No.2.23 admits Kähler-Ricci soliton and the Gromov-Hausdorff limit of the Kähler-Ricci flow must be a singular ℚ-Fano variety. This gives new examples of Fano manifolds of the lowest dimension on which Kähler-Ricci flow develops type II singularity.Ricci flowKähler–Ricci flowRicci solitonsKähler–Ricci solitonsSingularities3-manifoldsKähler geometryLimit spaces & RCD