Symbolic Rees algebras of space monomial primes of degree 5
Kazuhiko Kurano
TL;DR
This paper proves that the symbolic Rees algebra of a specific space monomial prime ideal of degree 5 is not finitely generated over a field of characteristic zero, highlighting a non-Noetherian property.
Contribution
It demonstrates for the first time that the symbolic Rees algebra of a particular space monomial prime of degree 5 is non-Noetherian.
Findings
Symbolic Rees algebra is not finitely generated
The ideal P_K(5,103,169) has a non-Noetherian symbolic Rees algebra
Provides a counterexample in the context of space monomial primes
Abstract
Let K be a field of characteristic 0. Let P_K(5,103,169) be the defining ideal of the space monomial curve {(t^5,t^{103},t^{169})}. In this paper we shall prove that the symbolic Rees algebra R_s(P_K(5,103,169)) is not Noetherian, that is, is not finitely generated over K.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic Geometry and Number Theory