On syzygies of Mori fibre spaces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914803570704384 |
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| author | He, Yang |
| author_facet | He, Yang |
| contents | We introduce homological and homotopical $r$-syzygies of Mori fibre spaces as a generalization of Sarkisov links and relations of Sarkisov links. For any proper morphism $Y/R$, we construct a contractible (if not empty) CW complex such that there is a 1-1 correspondence between its cells and the central models of $Y/R$. We derive from this CW complex a long exact sequence and a spectral sequence converging to the (co)homology of the relative birational automorphism group of $Y/R$. As an application, we compute the second group homology of the second Cremona group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_08609 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On syzygies of Mori fibre spaces He, Yang Algebraic Geometry We introduce homological and homotopical $r$-syzygies of Mori fibre spaces as a generalization of Sarkisov links and relations of Sarkisov links. For any proper morphism $Y/R$, we construct a contractible (if not empty) CW complex such that there is a 1-1 correspondence between its cells and the central models of $Y/R$. We derive from this CW complex a long exact sequence and a spectral sequence converging to the (co)homology of the relative birational automorphism group of $Y/R$. As an application, we compute the second group homology of the second Cremona group. |
| title | On syzygies of Mori fibre spaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2311.08609 |