On the strong Sarkisov program

2023/11/15 by He Yang, He, Yang · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2311.08750

openalex publication_date 2023/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We showed that the strong Sarkisov Program of dimension d can be derived from termination of specific log flips in dimension ≤ 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.

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