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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2411.07864 |
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| _version_ | 1866929589012398080 |
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| author | Delcroix, Thibaut |
| author_facet | Delcroix, Thibaut |
| contents | We prove that, for a spherical Fano threefold not in the Mori-Mukai family 2-29, and a weight function associated with the action of the connected center of a Levi subgroup of its automorphism group, weighted K-polystability is equivalent to vanishing of the weighted Futaki invariant. This is surprising since unlike the case of toric Fano manifold, there exist non-product, special, equivariant test configurations. For the Kähler-Einstein Fano threefold 2-29, and for well-chosen torus action on the three dimensional quadric, we show that this property is false and exhibit explicit examples of weighted optimal degenerations. We then generalize this to higher-dimensional quadrics and blowups of quadrics along a codimension 2 subquadric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07864 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weight sensitivity in K-stability of Fano varieties Delcroix, Thibaut Algebraic Geometry Complex Variables We prove that, for a spherical Fano threefold not in the Mori-Mukai family 2-29, and a weight function associated with the action of the connected center of a Levi subgroup of its automorphism group, weighted K-polystability is equivalent to vanishing of the weighted Futaki invariant. This is surprising since unlike the case of toric Fano manifold, there exist non-product, special, equivariant test configurations. For the Kähler-Einstein Fano threefold 2-29, and for well-chosen torus action on the three dimensional quadric, we show that this property is false and exhibit explicit examples of weighted optimal degenerations. We then generalize this to higher-dimensional quadrics and blowups of quadrics along a codimension 2 subquadric. |
| title | Weight sensitivity in K-stability of Fano varieties |
| topic | Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2411.07864 |