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On the strong Sarkisov program
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abstract
We showed that the strong Sarkisov Program of dimension $d$ can be derived from termination of specific log flips in dimension $\leq d-1$. As a corollary, we show that the strong Sarkisov Program holds in dimension 4. Additionally, we prove the weak Sarkisov program with decreasing (augmented) Sarkisov degree. Finally, using the theory of syzygies of Mori fibre spaces, we obtain a directed diagram that encodes all the information of the strong Sarkisov Program.
Forward citations
Cited by 2 Pith papers
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Effective termination of general type MMPs in dimension at most five
Every general type MMP in dimension at most five terminates; explicit step-count bounds are given in dimensions three and four.
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Sarkisov program for algebraically integrable and threefold foliations
The authors establish that for algebraically integrable foliations on klt varieties, and for rank one foliations on threefolds, any two Mori fiber spaces are connected by Sarkisov links.
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