English

On the strong Sarkisov program

Algebraic Geometry 2024-10-15 v2

Abstract

We showed that the strong Sarkisov Program of dimension dd can be derived from termination of specific log flips in dimension d1\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.

Cite

@article{arxiv.2311.08750,
  title  = {On the strong Sarkisov program},
  author = {Yang He},
  journal= {arXiv preprint arXiv:2311.08750},
  year   = {2024}
}
R2 v1 2026-06-28T13:21:45.025Z