K-polystability of Asymptotically Conical Kähler-Ricci Shrinkers
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908693309685760 |
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| author | Cifarelli, Charles Esparza, Carlos |
| author_facet | Cifarelli, Charles Esparza, Carlos |
| contents | Recently, Sun-Zhang have developed an algebraic theory for Kähler-Ricci shrinkers showing that they admit the structure of a polarized Fano fibration $(π: X \to Y, ξ)$. In particular, they conjecture that existence of a Kähler-Ricci shrinker metric is equivalent to a notion of K-stability. We prove one direction of this conjecture, namely that existence of a Kähler-Ricci shrinker metric $g$ implies K-polystability of $(π: X \to Y, ξ)$, in the case that the Ricci curvature of $g$ decays at infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03323 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | K-polystability of Asymptotically Conical Kähler-Ricci Shrinkers Cifarelli, Charles Esparza, Carlos Differential Geometry Algebraic Geometry Recently, Sun-Zhang have developed an algebraic theory for Kähler-Ricci shrinkers showing that they admit the structure of a polarized Fano fibration $(π: X \to Y, ξ)$. In particular, they conjecture that existence of a Kähler-Ricci shrinker metric is equivalent to a notion of K-stability. We prove one direction of this conjecture, namely that existence of a Kähler-Ricci shrinker metric $g$ implies K-polystability of $(π: X \to Y, ξ)$, in the case that the Ricci curvature of $g$ decays at infinity. |
| title | K-polystability of Asymptotically Conical Kähler-Ricci Shrinkers |
| topic | Differential Geometry Algebraic Geometry |
| url | https://arxiv.org/abs/2512.03323 |