Atomic decompositions for derived categories of G-surfaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911302249611264 |
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| author | Elagin, Alexey Schneider, Julia Shinder, Evgeny |
| author_facet | Elagin, Alexey Schneider, Julia Shinder, Evgeny |
| contents | We construct canonical semi-orthogonal decompositions for derived categories of smooth projective surfaces. These decompositions are compatible with the operations in the minimal model program, such as blow-ups and conic bundles. Therefore our construction confirms a conjecture of Kontsevich in dimension two. We work in the G-equivariant setting and over an arbitrary perfect field, and canonical decompositions are consistent with group change and algebraic field extensions. Our method is based on the G-minimal model program for surfaces and on the Sarkisov link factorisation of birational maps between Mori fibre spaces. We characterise rationality of surfaces, and in certain cases, birationality between surfaces in terms of the pieces of these decompositions, which we call atoms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05064 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Atomic decompositions for derived categories of G-surfaces Elagin, Alexey Schneider, Julia Shinder, Evgeny Algebraic Geometry 14F08, 14E08, 14E30 We construct canonical semi-orthogonal decompositions for derived categories of smooth projective surfaces. These decompositions are compatible with the operations in the minimal model program, such as blow-ups and conic bundles. Therefore our construction confirms a conjecture of Kontsevich in dimension two. We work in the G-equivariant setting and over an arbitrary perfect field, and canonical decompositions are consistent with group change and algebraic field extensions. Our method is based on the G-minimal model program for surfaces and on the Sarkisov link factorisation of birational maps between Mori fibre spaces. We characterise rationality of surfaces, and in certain cases, birationality between surfaces in terms of the pieces of these decompositions, which we call atoms. |
| title | Atomic decompositions for derived categories of G-surfaces |
| topic | Algebraic Geometry 14F08, 14E08, 14E30 |
| url | https://arxiv.org/abs/2512.05064 |