2009/03/03 by Masayuki Kawakita, Kawakita, Masayuki
Computer Science · Mathematics · Medicine · #14B05 #14E30 #14J17 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Calculus (dental) #Cryptography and Residue Arithmetic #Discrete mathematics #FOS: Mathematics #Mathematics #Medicine #Pure mathematics #Riemann hypothesis #math.AG #msc:14B05 #msc:14E30 #msc:14J17
paper · pdf · doi:10.48550/arxiv.0903.0418
11 pages
arxiv created 2009/03/03 · openalex publication_date 2009/03/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce an approach of Riemann--Roch theorem to the boundedness problem of minimal log discrepancies in fixed dimension. After reducing it to the case of a Gorenstein terminal singularity, firstly we prove that its minimal log discrepancy is bounded if either multiplicity or embedding dimension is bounded. Secondly we recover the characterisation of a Gorenstein terminal three-fold singularity by Reid, and the precise boundary of its minimal log discrepancy by Markushevich, without explicit classification. Finally we provide the precise boundary for a special four-fold singularity, whose general hyperplane section has a terminal piece.