Explicit Sarkisov program for regular surfaces over arbitrary fields and applications
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911221520793600 |
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| author | Bernasconi, Fabio Fanelli, Andrea Schneider, Julia Zimmermann, Susanna |
| author_facet | Bernasconi, Fabio Fanelli, Andrea Schneider, Julia Zimmermann, Susanna |
| contents | We prove the Sarkisov program for projective surfaces over excellent base rings, including the case of non-perfect base fields $k$ of characteristic $p>0$. We classify the Sarkisov links between Mori fibre spaces and their relations for regular surfaces, generalising work of Iskovskikh. As an application, we discuss rationality problems for regular surfaces and the structure of the plane Cremona group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03281 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit Sarkisov program for regular surfaces over arbitrary fields and applications Bernasconi, Fabio Fanelli, Andrea Schneider, Julia Zimmermann, Susanna Algebraic Geometry 14E07, 14E30, 14L99 We prove the Sarkisov program for projective surfaces over excellent base rings, including the case of non-perfect base fields $k$ of characteristic $p>0$. We classify the Sarkisov links between Mori fibre spaces and their relations for regular surfaces, generalising work of Iskovskikh. As an application, we discuss rationality problems for regular surfaces and the structure of the plane Cremona group. |
| title | Explicit Sarkisov program for regular surfaces over arbitrary fields and applications |
| topic | Algebraic Geometry 14E07, 14E30, 14L99 |
| url | https://arxiv.org/abs/2404.03281 |