2018/02/14 by H. Hauser, Hauser, Herwig, Stefan Perlega +1
Computer Science · Mathematics · #12D10 #14B05 #14E15 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1802.05010
openalex publication_date 2018/02/14 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We present a hypersurface singularity in positive characteristic which is\ndefined by a purely inseparable power series, and a sequence of point blowups\nso that, after applying the blowups to the singularity, the same type of\nsingularity reappears after the last blowup, with just certain exponents of the\ndefining power series shifted upwards. The construction hence yields a cycle.\nIterating this cycle leads to an infinite increase of the residual order of the\ndefining power series. This disproves a theorem claimed by Moh about the\nstability of the residual order under sequences of blowups. It is not a\ncounter-example to the resolution in positive characteristic since larger\ncenters are also permissible and prevent the phenomenon from happening.\n