Positivity of coinvariant divisors on $\overline{\mathrm{M}}_{0,n}$ and the parafermions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913906535956480 |
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| author | Chakravarty, Avik |
| author_facet | Chakravarty, Avik |
| contents | We give criteria for determining the positivity of line bundles coming from vertex operator algebras (VOAs) on the moduli space $\overline{\mathrm{M}}_{0,n}$ of rational curves with $n$ marked points. The criteria use the multiplicative structure of VOA representations encoded in the fusion ring. Using them, we construct positive line bundles on $\overline{\mathrm{M}}_{0,n}$ from certain parafermion VOAs. These give the first examples of commutant VOAs producing positive line bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17593 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Positivity of coinvariant divisors on $\overline{\mathrm{M}}_{0,n}$ and the parafermions Chakravarty, Avik Algebraic Geometry Quantum Algebra 14H10, 17B69 (primary), 81R10 (secondary) We give criteria for determining the positivity of line bundles coming from vertex operator algebras (VOAs) on the moduli space $\overline{\mathrm{M}}_{0,n}$ of rational curves with $n$ marked points. The criteria use the multiplicative structure of VOA representations encoded in the fusion ring. Using them, we construct positive line bundles on $\overline{\mathrm{M}}_{0,n}$ from certain parafermion VOAs. These give the first examples of commutant VOAs producing positive line bundles. |
| title | Positivity of coinvariant divisors on $\overline{\mathrm{M}}_{0,n}$ and the parafermions |
| topic | Algebraic Geometry Quantum Algebra 14H10, 17B69 (primary), 81R10 (secondary) |
| url | https://arxiv.org/abs/2506.17593 |