2018/04/05 by Youngsu Kim, Kim, Youngsu, Vivek Mukundan +1 · 1 citation
Computer Science · Mathematics · #13A30 #13D02 #13H15 #14A10 #14E05 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1804.02015
openalex publication_date 2018/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider the rational map ϕ: ℙn-1\mathbf k \stackrel[f0:⋯: fn]\longrightarrow ℙn\mathbf k defined by homogeneous polynomials f0,…,fn of the same degree d in a polynomial ring R=\mathbf k [x1,…,xn] over a field \mathbf k. Suppose I=(f0,…,fn) is a height two perfect ideal satisfying μ(Ip)≤dim Rp for p∈ Spec (R) ∖ V(x1,…, xn). We study the equations defining the graph of ϕ whose coordinate ring is the Rees algebra R[It]. We provide new methods to construct these equations using work of Buchsbaum and Eisenbud. Furthermore, for certain classes of ideals satisfying the conditions above, our methods lead to explicit equations defining Rees algebras of the ideals in these classes. These classes of examples are interesting, in that, there are no known methods to compute the defining ideal of the Rees algebra of such ideals. These new methods also give rise to effective criteria to check that ϕ is birational onto its image.