Automorphisms of the boundary complex of $\overline{\mathcal{M}}_{0, n}(\mathbb{P}^r, d)$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911564916850688 |
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| author | Joisha, Arjun Kannan, Siddarth |
| author_facet | Joisha, Arjun Kannan, Siddarth |
| contents | We compute the automorphism group of the dual complex $\mathsf{T}_{d, n}$ of the boundary divisor in the Kontsevich moduli space $\overline{\mathcal{M}}_{0, n}(\mathbb{P}^r, d)$. When $d \geq 2$, we find that $\mathrm{Aut}(\mathsf{T}_{d, n}) \cong \mathbb{S}_{n}$, while $\mathrm{Aut}(\mathsf{T}_{1, n}) \cong \mathbb{S}_{n + 1}$ for all $n \geq 4$. The complex $\mathsf{T}_{1, n}$ is also the dual complex of the boundary divisor in the Fulton--MacPherson compactification of the configuration space of $n$ points on $X$, if $X$ is any smooth, proper, and connected algebraic variety over $\mathbb{C}$. Following work of Massarenti, this implies that $\mathsf{T}_{1, n}$ admits automorphisms which in general do not extend to $X[n]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02970 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Automorphisms of the boundary complex of $\overline{\mathcal{M}}_{0, n}(\mathbb{P}^r, d)$ Joisha, Arjun Kannan, Siddarth Algebraic Geometry Combinatorics We compute the automorphism group of the dual complex $\mathsf{T}_{d, n}$ of the boundary divisor in the Kontsevich moduli space $\overline{\mathcal{M}}_{0, n}(\mathbb{P}^r, d)$. When $d \geq 2$, we find that $\mathrm{Aut}(\mathsf{T}_{d, n}) \cong \mathbb{S}_{n}$, while $\mathrm{Aut}(\mathsf{T}_{1, n}) \cong \mathbb{S}_{n + 1}$ for all $n \geq 4$. The complex $\mathsf{T}_{1, n}$ is also the dual complex of the boundary divisor in the Fulton--MacPherson compactification of the configuration space of $n$ points on $X$, if $X$ is any smooth, proper, and connected algebraic variety over $\mathbb{C}$. Following work of Massarenti, this implies that $\mathsf{T}_{1, n}$ admits automorphisms which in general do not extend to $X[n]$. |
| title | Automorphisms of the boundary complex of $\overline{\mathcal{M}}_{0, n}(\mathbb{P}^r, d)$ |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2604.02970 |