On the Kawaguchi--Silverman Conjecture for birational automorphisms of irregular varieties
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866929711081324544 |
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| author | Chen, Jungkai Alfred Lin, Hsueh-Yung Oguiso, Keiji |
| author_facet | Chen, Jungkai Alfred Lin, Hsueh-Yung Oguiso, Keiji |
| contents | We study the main open parts of the Kawaguchi--Silverman Conjecture, asserting that for a birational self-map $f$ of a smooth projective variety $X$ defined over $\overline{\mathbb Q}$, the arithmetic degree $α_f(x)$ exists and coincides with the first dynamical degree $δ_f$ for any $\overline{\mathbb Q}$-point $x$ of $X$ with a Zariski dense orbit. Among other results, we show that this holds when $X$ has Kodaira dimension zero and irregularity $q(X) \ge \dim X -1$ or $X$ is an irregular threefold (modulo one possible exception). We also study the existence of Zariski dense orbits, with explicit examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_09845 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Kawaguchi--Silverman Conjecture for birational automorphisms of irregular varieties Chen, Jungkai Alfred Lin, Hsueh-Yung Oguiso, Keiji Algebraic Geometry Dynamical Systems We study the main open parts of the Kawaguchi--Silverman Conjecture, asserting that for a birational self-map $f$ of a smooth projective variety $X$ defined over $\overline{\mathbb Q}$, the arithmetic degree $α_f(x)$ exists and coincides with the first dynamical degree $δ_f$ for any $\overline{\mathbb Q}$-point $x$ of $X$ with a Zariski dense orbit. Among other results, we show that this holds when $X$ has Kodaira dimension zero and irregularity $q(X) \ge \dim X -1$ or $X$ is an irregular threefold (modulo one possible exception). We also study the existence of Zariski dense orbits, with explicit examples. |
| title | On the Kawaguchi--Silverman Conjecture for birational automorphisms of irregular varieties |
| topic | Algebraic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2204.09845 |