2013/08/05 by Aiichi Yamasaki, Yamasaki, Aiichi · 1 citation
Computer Science · Engineering · Mathematics · #14E08 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #History and Theory of Mathematics #Polynomial and algebraic computation #math.AG #msc:14E08
paper · pdf · doi:10.48550/arxiv.1308.0909
22 pages
arxiv created 2013/08/05 · openalex publication_date 2013/08/05 · arxiv updated 2013/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The surface z2=ay2+P(x), a ∈ k, P(x) ∈ k[x] is not k-rational, if a \not∈ k2 and P(x) satisfies some conditions. This result essentially due to Iskovskih but his statement is in terms of algebraic geometry, and not so easy to access for the researchers of the field extension. This paper aims to give a formulation accessible more easily. A necessary and sufficient condition for k-rationality is given in terms of a and P, assuming that \ch k \not= 2 and every irreducible component of P(x) is separable over k.