K-stability of special Gushel-Mukai manifolds
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| Format: | Preprint |
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2024
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| _version_ | 1866917106716508160 |
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| author | Liu, Yuchen Wang, Linsheng |
| author_facet | Liu, Yuchen Wang, Linsheng |
| contents | Gushel-Mukai manifolds are specific families of $n$-dimensional Fano manifolds of Picard rank $1$ and index $n-2$ where $3\leq n \leq 6$. 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 $3\leq n\leq 6$. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_10797 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | K-stability of special Gushel-Mukai manifolds Liu, Yuchen Wang, Linsheng Algebraic Geometry Differential Geometry 14J45, 32Q20, 14D20 Gushel-Mukai manifolds are specific families of $n$-dimensional Fano manifolds of Picard rank $1$ and index $n-2$ where $3\leq n \leq 6$. 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 $3\leq n\leq 6$. 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. |
| title | K-stability of special Gushel-Mukai manifolds |
| topic | Algebraic Geometry Differential Geometry 14J45, 32Q20, 14D20 |
| url | https://arxiv.org/abs/2405.10797 |