On the birational isotriviality of the Albanese morphism of a log Calabi-Yau pair with a torus action
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910031060926464 |
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| author | Rösler, Linus |
| author_facet | Rösler, Linus |
| contents | Let $(X,Δ)$ be a projective, log canonical, $K$-trivial pair over the complex numbers. Let $Z$ be a minimal log canonical center of $(X,Δ)$ and suppose that there exists a torus $\mathbb{T}\subseteq\operatorname{Aut}(X)$ preserving $Δ$ and such that $\dim\mathbb{T}=\operatorname{codim}_X Z$. Then we show that two general fibers of the Albanese morphism $\operatorname{alb}_X$ are birationally equivalent. In particular, the pathological example of a projective, log canonical, $K$-trivial variety whose Albanese morphism is not generically birationally isotrivial, recently constructed by Bernasconi, Filipazzi, Patakfalvi and Tsakanikas, can be avoided under the additional hypothesis that there exists a torus of large enough dimension in the automorphism group of the given pair. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20027 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the birational isotriviality of the Albanese morphism of a log Calabi-Yau pair with a torus action Rösler, Linus Algebraic Geometry 14E99, 14J32, 14J40, 14K99, 14L30 (Primary) 14D06, 14E30 (Secondary) Let $(X,Δ)$ be a projective, log canonical, $K$-trivial pair over the complex numbers. Let $Z$ be a minimal log canonical center of $(X,Δ)$ and suppose that there exists a torus $\mathbb{T}\subseteq\operatorname{Aut}(X)$ preserving $Δ$ and such that $\dim\mathbb{T}=\operatorname{codim}_X Z$. Then we show that two general fibers of the Albanese morphism $\operatorname{alb}_X$ are birationally equivalent. In particular, the pathological example of a projective, log canonical, $K$-trivial variety whose Albanese morphism is not generically birationally isotrivial, recently constructed by Bernasconi, Filipazzi, Patakfalvi and Tsakanikas, can be avoided under the additional hypothesis that there exists a torus of large enough dimension in the automorphism group of the given pair. |
| title | On the birational isotriviality of the Albanese morphism of a log Calabi-Yau pair with a torus action |
| topic | Algebraic Geometry 14E99, 14J32, 14J40, 14K99, 14L30 (Primary) 14D06, 14E30 (Secondary) |
| url | https://arxiv.org/abs/2602.20027 |