2006/12/21 by D. Rogalski, Rogalski, D., J. T. Stafford +1
Mathematics · #14A22 #16P40 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:14A22 #msc:16P40
paper · pdf · doi:10.48550/arxiv.math/0612658
arxiv created 2006/12/21 · openalex publication_date 2006/12/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In an earlier paper (D. S. Keeler, D. Rogalski, and J. T. Stafford, ``Naive noncommutative blowing up,'' Duke Math. J., 126 (2005), 491-546), we defined and investigated the properties of the naive blowup of an integral projective scheme X at a single closed point. In this paper we extend those results to the case when one naively blows up X at any suitably generic zero-dimensional subscheme Z. The resulting algebra A has a number of curious properties; for example it is noetherian but never strongly noetherian and the point modules are never parametrized by a projective scheme. This is despite the fact that the category of torsion modules in the quotient category qgr A is equivalent to the category of torsion coherent sheaves over X. These results are used in the companion paper ``A class of noncommutative projective surfaces'' to prove that a large class of noncommutative surfaces can be written as naive blowups.