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arXiv · 2311.08609

On syzygies of Mori fibre spaces

Yang He
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Abstract

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.

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Yang He. 2023-11-15. On syzygies of Mori fibre spaces. https://arxiv.org/abs/2311.08609

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