Dynamics of Projectivized Toric Vector Bundles
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909878643064832 |
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| author | González-Anaya, Javier Nasserden, Brett Zotine, Sasha |
| author_facet | González-Anaya, Javier Nasserden, Brett Zotine, Sasha |
| contents | We study surjective endomorphisms of projective bundles over toric varieties, achieving three main results. First, we provide a structural theorem describing endomorphisms of projectivized split bundles over arbitrary base varieties, which we use to classify all surjective endomorphisms of Hirzebruch surfaces and construct novel families of examples. Second, for non-split equivariant bundles over toric varieties, we prove that the dynamical degree of an endomorphism of the projectivization is controlled by the base morphism; as a consequence, we establish the Kawaguchi--Silverman conjecture for such bundles. Third, using an explicit transition function method, we prove that projectivizations of tangent and cotangent bundles of smooth toric varieties admit no non-automorphic surjective endomorphisms commuting with toric morphisms on the base. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26757 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics of Projectivized Toric Vector Bundles González-Anaya, Javier Nasserden, Brett Zotine, Sasha Algebraic Geometry 37P55, 14J60, 14M25 We study surjective endomorphisms of projective bundles over toric varieties, achieving three main results. First, we provide a structural theorem describing endomorphisms of projectivized split bundles over arbitrary base varieties, which we use to classify all surjective endomorphisms of Hirzebruch surfaces and construct novel families of examples. Second, for non-split equivariant bundles over toric varieties, we prove that the dynamical degree of an endomorphism of the projectivization is controlled by the base morphism; as a consequence, we establish the Kawaguchi--Silverman conjecture for such bundles. Third, using an explicit transition function method, we prove that projectivizations of tangent and cotangent bundles of smooth toric varieties admit no non-automorphic surjective endomorphisms commuting with toric morphisms on the base. |
| title | Dynamics of Projectivized Toric Vector Bundles |
| topic | Algebraic Geometry 37P55, 14J60, 14M25 |
| url | https://arxiv.org/abs/2510.26757 |