On the strong Sarkisov program

arxiv（2023）

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Abstract

We showed that the strong Sarkisov Program of dimension $d$ can be derived from termination of certain log flips in dimension $\leq d-1$. As a corollary, we show that the strong Sarkisov Program holds in dimension 4. Using the theory of syzygies of Mori fibre spaces, we obtain a directed diagram that encodes all the information of the strong Sarkisov Program.

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