On the shape of the K-semistable domain and wall crossing for K-stability
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910251041685504 |
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| author | Zhou, Chuyu |
| author_facet | Zhou, Chuyu |
| contents | Fixing two positive integers $d$ and $k$, a positive number $v$, and a positive integer $I$, we prove that the K-semistable domain of the log pair $(X, \sum_{j=1}^kD_j)$ is a rational polytope lying in the $k$-dimensional simplex $\overline{Δ^k}$, where $X$ is a Fano variety of dimension $d$, $D_j\sim_\mathbb{Q} -K_X$, $(-K_X)^d=v$, $I(K_X+D_j)\sim 0$, and $(X, \sum_{j=1}^kc_jD_j)$ is a K-semistable log Fano pair for some $c_j\in [0,1)\cap \mathbb{Q}$. Moreover, we show that there are only finitely many polytopes which may appear as the K-semistable domains for such log pairs. Based on this, we establish a wall crossing theory for K-moduli with multiple boundaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_13503 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the shape of the K-semistable domain and wall crossing for K-stability Zhou, Chuyu Algebraic Geometry Fixing two positive integers $d$ and $k$, a positive number $v$, and a positive integer $I$, we prove that the K-semistable domain of the log pair $(X, \sum_{j=1}^kD_j)$ is a rational polytope lying in the $k$-dimensional simplex $\overline{Δ^k}$, where $X$ is a Fano variety of dimension $d$, $D_j\sim_\mathbb{Q} -K_X$, $(-K_X)^d=v$, $I(K_X+D_j)\sim 0$, and $(X, \sum_{j=1}^kc_jD_j)$ is a K-semistable log Fano pair for some $c_j\in [0,1)\cap \mathbb{Q}$. Moreover, we show that there are only finitely many polytopes which may appear as the K-semistable domains for such log pairs. Based on this, we establish a wall crossing theory for K-moduli with multiple boundaries. |
| title | On the shape of the K-semistable domain and wall crossing for K-stability |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2302.13503 |