Explicit Sarkisov program for regular surfaces over arbitrary fields and applications. arXiv:2404.03281
Preprint, arXiv:2404.03281 [math.AG] (2024).
Summary: We prove the Sarkisov program for projective surfaces over excellent base rings, including the case of non-perfect base fields 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.
MSC:
| 14E07 | Birational automorphisms, Cremona group and generalizations |
| 14E30 | Minimal model program (Mori theory, extremal rays) |
| 14L99 | Algebraic groups |
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