A birational version of K-stability for big classes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
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| _version_ | 1866915892785315840 |
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| author | Dervan, Ruadhaí Reboulet, Rémi |
| author_facet | Dervan, Ruadhaí Reboulet, Rémi |
| contents | We introduce a theory of uniform K-stability for big line bundles on smooth projective varieties. This extends the existing theory both for varieties with ample line bundles, and for varieties with big anticanonical class. Our main result gives a valuative characterisation of uniform K-stability, through finite collections of divisorial valuations. We further prove that uniform K-stability is preserved under pullbacks and certain pushforwards, which implies that uniform K-stability is well-defined at the level of b-divisors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25605 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A birational version of K-stability for big classes Dervan, Ruadhaí Reboulet, Rémi Algebraic Geometry We introduce a theory of uniform K-stability for big line bundles on smooth projective varieties. This extends the existing theory both for varieties with ample line bundles, and for varieties with big anticanonical class. Our main result gives a valuative characterisation of uniform K-stability, through finite collections of divisorial valuations. We further prove that uniform K-stability is preserved under pullbacks and certain pushforwards, which implies that uniform K-stability is well-defined at the level of b-divisors. |
| title | A birational version of K-stability for big classes |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2603.25605 |