Picard rank jumps for families of K3 surfaces in positive characteristic
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911540844691456 |
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| author | Jiang, Ruofan Shankar, Ananth N. Yang, Ziquan |
| author_facet | Jiang, Ruofan Shankar, Ananth N. Yang, Ziquan |
| contents | Let X/C be a non iso-trivial family of K3 surfaces over a curve C defined over characteristic p > 2 field. We show that if X avoids a necessary and structural obstruction coming from Frobenius, and satisfies a big monodromy condition, then there are infinitely may geometric fibers that have larger Picard rank than the geometric generic fiber. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22678 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Picard rank jumps for families of K3 surfaces in positive characteristic Jiang, Ruofan Shankar, Ananth N. Yang, Ziquan Algebraic Geometry Number Theory Let X/C be a non iso-trivial family of K3 surfaces over a curve C defined over characteristic p > 2 field. We show that if X avoids a necessary and structural obstruction coming from Frobenius, and satisfies a big monodromy condition, then there are infinitely may geometric fibers that have larger Picard rank than the geometric generic fiber. |
| title | Picard rank jumps for families of K3 surfaces in positive characteristic |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2603.22678 |