Polarized endomorphisms of log Calabi-Yau pairs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909742148878336 |
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| author | Moraga, Joaquín Yáñez, José Ignacio Yeong, Wern |
| author_facet | Moraga, Joaquín Yáñez, José Ignacio Yeong, Wern |
| contents | Let $(X,Δ)$ be a dlt log Calabi-Yau pair admitting a polarized endomorphism. We show that $(X,Δ)$ is a finite quotient of a toric log Calabi-Yau fibration over an abelian variety. We provide an example which shows that the previous statement does not hold if we drop the dlt condition of $(X,Δ)$ even if $X$ is a smooth variety. Given a klt type variety $X$ and a log Calabi-Yau pair $(X,Δ)$ admitting a polarized endomorphism, we show that a suitable birational modification of $(X,Δ)$ is a finite quotient of a toric log Calabi-Yau fibration over an abelian variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18092 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polarized endomorphisms of log Calabi-Yau pairs Moraga, Joaquín Yáñez, José Ignacio Yeong, Wern Algebraic Geometry Primary 08A35, 14M25, Secondary 14F35 Let $(X,Δ)$ be a dlt log Calabi-Yau pair admitting a polarized endomorphism. We show that $(X,Δ)$ is a finite quotient of a toric log Calabi-Yau fibration over an abelian variety. We provide an example which shows that the previous statement does not hold if we drop the dlt condition of $(X,Δ)$ even if $X$ is a smooth variety. Given a klt type variety $X$ and a log Calabi-Yau pair $(X,Δ)$ admitting a polarized endomorphism, we show that a suitable birational modification of $(X,Δ)$ is a finite quotient of a toric log Calabi-Yau fibration over an abelian variety. |
| title | Polarized endomorphisms of log Calabi-Yau pairs |
| topic | Algebraic Geometry Primary 08A35, 14M25, Secondary 14F35 |
| url | https://arxiv.org/abs/2406.18092 |