https://neckpinch.com/authors/yuchen-liu/New arXiv papers by Yuchen Liu, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2405.10797/arxiv:2405.10797Fri, 17 May 2024 00:00:00 GMTYuchen Liu, Linsheng Wang — Gushel-Mukai manifolds are specific families of n-dimensional Fano manifolds of Picard rank 1 and index n-2 where 3≤ n ≤ 6. A Gushel-Mukai n-fold is either ordinary, i.e. a hyperquadric section of a quintic Del Pezzo (n+1)-fold, or special, i.e. it admits a double cover over the quintic Del Pezzo n-fold branched along an ordinary Gushel-Mukai (n-1)-fold. In this paper, we prove that a general special Gushel-Mukai n-fold is K-stable for every 3≤ n≤ 6. Furthermore, we give a description of the first and last walls of the K-moduli of the pair (M,cQ), where M is the quintic Del Pezzo fourfold (or fivefold) and Q is an ordinary Gushel-Mukai threefold (or fourfold). Besides, we compute δ-invariants of quintic Del Pezzo fourfolds and fivefolds which were shown to be K-unstable by K. Fujita, and show that they admit Kähler-Ricci solitons.Ricci solitonsKähler–Ricci solitons3-manifoldsKähler geometryStability & uniquenessKähler–Einstein & K-stability