Minimal log discrepancy and orbifold curves
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912233993273344 |
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| author | Li, Chi Zhou, Zhengyi |
| author_facet | Li, Chi Zhou, Zhengyi |
| contents | We show that the minimal log discrepancy of any isolated Fano cone singularity is at most the dimension of the variety. This is based on its relation with dimensions of moduli spaces of orbifold rational curves. We also propose a conjectural characterization of weighted projective spaces as Fano orbifolds in terms of orbifold rational curves, which would imply the equality holds only for smooth points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11847 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal log discrepancy and orbifold curves Li, Chi Zhou, Zhengyi Algebraic Geometry Symplectic Geometry We show that the minimal log discrepancy of any isolated Fano cone singularity is at most the dimension of the variety. This is based on its relation with dimensions of moduli spaces of orbifold rational curves. We also propose a conjectural characterization of weighted projective spaces as Fano orbifolds in terms of orbifold rational curves, which would imply the equality holds only for smooth points. |
| title | Minimal log discrepancy and orbifold curves |
| topic | Algebraic Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2502.11847 |