2009/08/08 by Shihoko Ishii, Ishii, Shihoko, Joerg Winkelmann +1 · 1 citation
Mathematics · Physics and Astronomy · #14B05 #14J10 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #math.AG #msc:14B05 #msc:14J10
paper · pdf · doi:10.48550/arxiv.0908.1146
6 pages, to appear in Canadian Comptes Rendus
arxiv created 2009/08/08 · openalex publication_date 2009/08/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If two schemes are isomorphic, then their m-jet schemes are isomorphic for all m. In this paper we consider the converse problem. We prove that if an isomorphism of the m-jet schemes is induced from a morphism of the base schemes, then the morphism of the base schemes is an isomorphism. But we also prove that just the existence of isomorphisms between m-jet schemes does not yield the existence of an isomorphism between the base schemes.