Counting rational points on Hirzebruch-Kleinschmidt varieties over global function fields
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| Format: | Preprint |
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2024
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| _version_ | 1866913513363996672 |
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| author | Herrero, Sebastián Martínez, Tobías Montero, Pedro |
| author_facet | Herrero, Sebastián Martínez, Tobías Montero, Pedro |
| contents | Inspired by Bourqui's work on anticanonical height zeta functions on Hirzebruch surfaces, we study height zeta functions of split toric varieties with Picard rank 2 over global function fields, with respect to height functions associated with big metrized line bundles. We show that these varieties can be naturally decomposed into a finite disjoint union of subvarieties, where precise analytic properties of the corresponding height zeta functions can be given. As application, we obtain asymptotic formulas for the number of rational points of large height on each subvariety, with explicit leading constants and controlled error terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07631 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting rational points on Hirzebruch-Kleinschmidt varieties over global function fields Herrero, Sebastián Martínez, Tobías Montero, Pedro Number Theory Algebraic Geometry 14G05, 11G50, 11M41 (primary), 14M25, 11G35 (secondary) Inspired by Bourqui's work on anticanonical height zeta functions on Hirzebruch surfaces, we study height zeta functions of split toric varieties with Picard rank 2 over global function fields, with respect to height functions associated with big metrized line bundles. We show that these varieties can be naturally decomposed into a finite disjoint union of subvarieties, where precise analytic properties of the corresponding height zeta functions can be given. As application, we obtain asymptotic formulas for the number of rational points of large height on each subvariety, with explicit leading constants and controlled error terms. |
| title | Counting rational points on Hirzebruch-Kleinschmidt varieties over global function fields |
| topic | Number Theory Algebraic Geometry 14G05, 11G50, 11M41 (primary), 14M25, 11G35 (secondary) |
| url | https://arxiv.org/abs/2408.07631 |