The minimal volume of stable surfaces of rank one
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911669221851136 |
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| author | Liu, Jihao Liu, Wenfei |
| author_facet | Liu, Jihao Liu, Wenfei |
| contents | We determine the minimal volume of a stable surface of rank one, and show that the surface attaining this minimum is unique up to isomorphism. This resolves a conjecture of Alexeev and the second author.
Of independent interest, the decisive step of the proof uses a plurigenus inequality re-derived by an AI chatbot and applied as a pluricanonical filter; we further apply this filter to rule out additional cases in the classification of small-volume threefolds of general type, and in Kollár's algebraic Montgomery--Yang problem. The underlying inequality has classical antecedents. To our knowledge this is the first paper in birational geometry to claim a C2-level human--AI collaboration in the sense of Feng et al., where the AI's contribution is the recognition that this inequality functions as the decisive pluricanonical filter in the basket analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05641 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The minimal volume of stable surfaces of rank one Liu, Jihao Liu, Wenfei Algebraic Geometry 14J29, 14J17, 14E30, 14J10, 14B05, 68V05, 68T05, 68U35 We determine the minimal volume of a stable surface of rank one, and show that the surface attaining this minimum is unique up to isomorphism. This resolves a conjecture of Alexeev and the second author. Of independent interest, the decisive step of the proof uses a plurigenus inequality re-derived by an AI chatbot and applied as a pluricanonical filter; we further apply this filter to rule out additional cases in the classification of small-volume threefolds of general type, and in Kollár's algebraic Montgomery--Yang problem. The underlying inequality has classical antecedents. To our knowledge this is the first paper in birational geometry to claim a C2-level human--AI collaboration in the sense of Feng et al., where the AI's contribution is the recognition that this inequality functions as the decisive pluricanonical filter in the basket analysis. |
| title | The minimal volume of stable surfaces of rank one |
| topic | Algebraic Geometry 14J29, 14J17, 14E30, 14J10, 14B05, 68V05, 68T05, 68U35 |
| url | https://arxiv.org/abs/2605.05641 |