Line bundles on Contractions of $\overline{\rm{M}}_{0,n}$ via Coinvariant Divisors
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908713480093696 |
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| author | Choi, Daebeom |
| author_facet | Choi, Daebeom |
| contents | Using representations of vertex operator algebras, we describe the line bundles on a wide range of contractions of $\overline{\rm{M}}_{0,n}$, the moduli space of stable $n$-pointed rational curves, by proving a stronger version of the contraction theorem for these morphisms. These include the celebrated constructions of Kapranov, Keel, and Knudsen. Our main result suggests that while many so-called F-curves are not $K_X$-negative, they exhibit behavior similar to $K_X$-negative curves. This reveals for instance, a distinguished property of Knudsen's construction $f_{\text{Knu}}:\overline{\rm{M}}_{0,n}\to \overline{\rm{M}}_{0,n-1}\times_{\overline{\rm{M}}_{0,n-2}}\overline{\rm{M}}_{0,n-1}$, allowing for the classification of all possible factorizations of $f_{\text{Knu}}$, as well as further applications, and generalizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10860 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Line bundles on Contractions of $\overline{\rm{M}}_{0,n}$ via Coinvariant Divisors Choi, Daebeom Algebraic Geometry Quantum Algebra 14H10, 17B69 (primary), 81R10 (secondary) Using representations of vertex operator algebras, we describe the line bundles on a wide range of contractions of $\overline{\rm{M}}_{0,n}$, the moduli space of stable $n$-pointed rational curves, by proving a stronger version of the contraction theorem for these morphisms. These include the celebrated constructions of Kapranov, Keel, and Knudsen. Our main result suggests that while many so-called F-curves are not $K_X$-negative, they exhibit behavior similar to $K_X$-negative curves. This reveals for instance, a distinguished property of Knudsen's construction $f_{\text{Knu}}:\overline{\rm{M}}_{0,n}\to \overline{\rm{M}}_{0,n-1}\times_{\overline{\rm{M}}_{0,n-2}}\overline{\rm{M}}_{0,n-1}$, allowing for the classification of all possible factorizations of $f_{\text{Knu}}$, as well as further applications, and generalizations. |
| title | Line bundles on Contractions of $\overline{\rm{M}}_{0,n}$ via Coinvariant Divisors |
| topic | Algebraic Geometry Quantum Algebra 14H10, 17B69 (primary), 81R10 (secondary) |
| url | https://arxiv.org/abs/2404.10860 |