2002/09/12 by Klaus Altmann, Bernd Sturmfels, Altmann, Klaus +1
Computer Science · Mathematics · #13P10 (Primary) 14L30 #52B70 (Secondary) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #msc:13P10 #msc:14L30 #msc:52B70
paper · pdf · doi:10.48550/arxiv.math/0209152
15 pages, Latex
arxiv created 2002/09/12 · openalex publication_date 2002/09/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There is a natural infinite graph whose vertices are the monomial ideals in a polynomial ring. The definition involves Gröbner bases or the action of an algebraic torus. We present algorithms for computing the (affine schemes representing) edges in this graph. We study the induced subgraphs on multigraded Hilbert schemes and on square-free monomial ideals. In the latter case, the edges correspond to generalized bistellar flips.