Dynamics of Endomorphisms for Projective Bundles on Elliptic Curves
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912528420831232 |
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| author | Nasserden, Brett Zotine, Sasha |
| author_facet | Nasserden, Brett Zotine, Sasha |
| contents | We study the dynamics of surjective endomorphisms of projective bundles on elliptic curves and relate their dynamical properties to the geometry of the bundle. As an application we prove the Kawaguchi--Silverman conjecture for projective bundles on elliptic curves, thereby completing the conjecture for all projective bundles on curves. Our approach is to use the transition functions of the bundles. This allows us to further prove the conjecture for projective split bundles on a smooth projective variety with finitely generated Mori cone. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03313 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dynamics of Endomorphisms for Projective Bundles on Elliptic Curves Nasserden, Brett Zotine, Sasha Algebraic Geometry 37P30, 37P55 (Primary) 14H60 (Secondary) We study the dynamics of surjective endomorphisms of projective bundles on elliptic curves and relate their dynamical properties to the geometry of the bundle. As an application we prove the Kawaguchi--Silverman conjecture for projective bundles on elliptic curves, thereby completing the conjecture for all projective bundles on curves. Our approach is to use the transition functions of the bundles. This allows us to further prove the conjecture for projective split bundles on a smooth projective variety with finitely generated Mori cone. |
| title | Dynamics of Endomorphisms for Projective Bundles on Elliptic Curves |
| topic | Algebraic Geometry 37P30, 37P55 (Primary) 14H60 (Secondary) |
| url | https://arxiv.org/abs/2310.03313 |