Noetherian Rees Algebra and Symbolic Powers
Let R be a field and p be the kernel of the homomorphism ϕ from R[[x,y,z]] to R[[t]] defined by: (x → tm1,y→tm2,z→ tm3 ). One wishes to know whether the symbolic Rees algebra of p,Rs p=⨁ n≥0p ntn is Noetherian. Consider the case when p = (xα+α' – y2z, y4 – xαz, z 2 – xα'y2). We show the symbolic Rees algebra of p,Rsp =⨁n≥0 pn tn is Noetherian for p (m1, m2, m3) when m1 = 6, m2 = 2α + α', and m 3 = 2α + 4α'.^
"Noetherian Rees Algebra and Symbolic Powers"
ETD Collection for Tennessee State University.