The dual complex of $\mathcal{M}_{1,n}(\mathbb{P}^r,d)$ via the geometry of the Vakil--Zinger moduli space
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912937740861440 |
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| author | Kannan, Siddarth Song, Terry Dekun |
| author_facet | Kannan, Siddarth Song, Terry Dekun |
| contents | We study normal crossings compactifications of the moduli space of maps $\mathcal{M}_{g, n}(\mathbb{P}^r, d)$, for $g = 0$ and $g = 1$. In each case we explicitly determine the dual boundary complex, and prove that it admits a natural interpretation as a moduli space of decorated metric graphs. We prove that the dual complexes are contractible when $r \geq 1$ and $d > g$. When $g = 1$, our result depends on a new understanding of the connected components of boundary strata in the Vakil--Zinger desingularization and its modular interpretation by Ranganathan--Santos-Parker--Wise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03518 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The dual complex of $\mathcal{M}_{1,n}(\mathbb{P}^r,d)$ via the geometry of the Vakil--Zinger moduli space Kannan, Siddarth Song, Terry Dekun Algebraic Geometry Combinatorics We study normal crossings compactifications of the moduli space of maps $\mathcal{M}_{g, n}(\mathbb{P}^r, d)$, for $g = 0$ and $g = 1$. In each case we explicitly determine the dual boundary complex, and prove that it admits a natural interpretation as a moduli space of decorated metric graphs. We prove that the dual complexes are contractible when $r \geq 1$ and $d > g$. When $g = 1$, our result depends on a new understanding of the connected components of boundary strata in the Vakil--Zinger desingularization and its modular interpretation by Ranganathan--Santos-Parker--Wise. |
| title | The dual complex of $\mathcal{M}_{1,n}(\mathbb{P}^r,d)$ via the geometry of the Vakil--Zinger moduli space |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2411.03518 |