p-lck with potential structure on LVMB manifolds
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914100914683904 |
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| author | Faucard, Bastien |
| author_facet | Faucard, Bastien |
| contents | In this paper, I present a natural generalization of all the results from [6] to LVMB manifolds: to summarize, very few LVMB manifolds are lck, and none are lck with potential except for diagonal Hopf manifolds. Moreover, if $N$ is an LVMB manifold with a sufficient number of indispensable coordinates, and under a certain assumption $(H)$ (which may be artificial, as I conjecture) on the localization of the configuration $Λ$, there exists a non-compact and non-Kählerian $\mathbb{Z}^p$-lck with potential cover of $N$ with $p = m-1$. Furthermore, I show that the conjecture stated at the end of [5] (that $p$ is bounded below by $m-1$) is false, by exhibiting examples of LVMB manifolds that are $1$-lck with potential when $m\geq 3$ and $n>2m+1$. This leads to the formulation of a new conjecture: if assumption $(H)$ holds, then $N$ is $1$-lck with potential. Moreover, assumption $(H)$ seems entirely artificial. This conjecture is supported by several examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16181 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | p-lck with potential structure on LVMB manifolds Faucard, Bastien Differential Geometry Complex Variables In this paper, I present a natural generalization of all the results from [6] to LVMB manifolds: to summarize, very few LVMB manifolds are lck, and none are lck with potential except for diagonal Hopf manifolds. Moreover, if $N$ is an LVMB manifold with a sufficient number of indispensable coordinates, and under a certain assumption $(H)$ (which may be artificial, as I conjecture) on the localization of the configuration $Λ$, there exists a non-compact and non-Kählerian $\mathbb{Z}^p$-lck with potential cover of $N$ with $p = m-1$. Furthermore, I show that the conjecture stated at the end of [5] (that $p$ is bounded below by $m-1$) is false, by exhibiting examples of LVMB manifolds that are $1$-lck with potential when $m\geq 3$ and $n>2m+1$. This leads to the formulation of a new conjecture: if assumption $(H)$ holds, then $N$ is $1$-lck with potential. Moreover, assumption $(H)$ seems entirely artificial. This conjecture is supported by several examples. |
| title | p-lck with potential structure on LVMB manifolds |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2510.16181 |