2024/03/02 by Bingyi Chen, Chen, Bingyi · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2403.01154
openalex publication_date 2024/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (X,B) be an ε-lc pair of dimension d with a closed point x∈ X. Birkar and Shokurov conjectured that there is an effective Cartier divisor H passing through x such that (X,B+tH) is lc near x, where t is a positive real number depending only on d,ε. We prove that this conjecture is equivalent to Shokurov's conjecture on boundedness of klt complements on Fano fibrations and we confirm it in dimension 2. As a corollary, we prove the boundedness of klt complements on Fano fibrations over surfaces.