2015/02/25 by Yuki Tanaka, Tanaka, Yuki
Mathematics · #14B05 #14B07 #14J17 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14B05 #msc:14B07 #msc:14J17
paper · pdf · doi:10.48550/arxiv.1502.07236
27 pages, a master's thesis in Grad. School of Math. Sci., Univ. of Tokyo
arxiv created 2015/02/25 · arxiv updated 2015/02/26
The weighted dual graph of a two-dimensional normal singularity (X, x) represents the topological nature of the exceptional locus of its minimal log resolution. (X, x) and its graph are said to be taut if the singularity can be uniquely determined by the graph. Laufer gave a complete list of taut singularities over ℂ. In positive characteristics, taut graphs over ℂ are not necessarily taut and tautness have been studied only for special cases. In this paper, we prove the tautness of F-regular singularities. We also discuss the tautness of F-pure rational singularities.