2024/12/24 by Ayçin Iplikçi Arodirik, Arodirik, Ayçin Iplikçi
Mathematics · #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2412.18694
openalex publication_date 2024/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper presents a technique for viewing quasi-coherent sheaves of ideals of a given blowup as regular ideals of a ring. In the paper, we first describe (Zariski) models as integral schemes that are separated and of finite type over an integral domain D. We then construct a ring D^* for a given projective model (e.g. blowup of D over a finitely generated ideal) by intersecting Nagata function rings. The spectrum of D^* contains the projective model, but similar to the Proj-construction, it includes additional prime ideals. We characterize the relevant ideals and construct a faithfully flat morphism of schemes from the spectrum of D^* to the model. Finally, using Abhyankar's definition of ideals on models, we identify the relevant ideals of D^* with the quasi-coherent sheaves of ideals of the corresponding projective model.