2005/05/01 by Osamu Fujino · 18 citations
Mathematics · Physics and Astronomy · Computer Science · #Algebraic Geometry and Number Theory #Nonlinear Waves and Solitons #Polynomial and algebraic computation #Cone (formal languages) #Construct (python library) #Physics #Variety (cybernetics) #Simple (philosophy) #Pure mathematics #Projective test #Mathematics #Computer science #Philosophy #Algorithm #Statistics
paper · pdf · doi:10.3792/pjaa.81.80
published in Proceedings of the Japan Academy Series A Mathematical Sciences 81(5) (Institute of Mathematical Statistics)
openalex publication_date 2005/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Kleiman-Mori cone plays important roles in the birational geometry. In this paper, we construct complete varieties whose Kleiman-Mori cones have interesting properties. First, we construct a simple and explicit example of complete non-projective singular varieties for which Kleiman's ampleness criterion does not hold. More precisely, we construct a complete non-projective toric variety X and a line bundle L on X such that L is positive on NE(X)∖ \0\. Next, we construct complete singular varieties X with NE(X)=N1(X)≃ Rk for any k. These explicit examples seem to be missing in the literature.