2023/11/02 by Bingyi Chen, Chen, Bingyi
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2311.00985
openalex publication_date 2023/11/02 · openalex created_date 2023/11/04 · openalex updated_date 2026/07/28
It was conjectured by M\textsuperscriptcKernan and Shokurov that for any Fano contraction f:X → Z of relative dimension r with X being ε-lc, there is a positive δ depending only on r,ε such that Z is δ-lc and the multiplicity of the fiber of f over a codimension one point of Z is bounded from above by 1/δ. Recently, this conjecture was confirmed by Birkar \citeBi23. In this paper, we give an explicit value for δ in terms of ε,r in the toric case, which belongs to O(ε2r) as ε→ 0. The order O(ε2r) is optimal in some sense.