Year: 2026
Type: preprint
Abstract: We prove that if two parameterizations of a complete reduced noetherian curve over an algebraically closed field agree modulo a sufficiently large power of the maximal ideal, then the two parameterizations are equivalent. This strengthens some bounds from Greuel and Pfister. In addition, we prove that if two reduced and irreducible curve singularities are isomorphic modulo sufficiently high (and identical) powers of their respective maximal ideals, then the completions of the two curves are isomorphic, and the isomorphism of the full completions agrees with the original isomorphism modulo some lower power of the maximal ideals. We provide a new and better bound on the lower power, strengthening the bound in Hironaka
Source: arXiv (Cornell University)
Authors: Hübl, Reinhold, Swanson, Irena
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203867143