Finite Generation of Algebras Associated to Powers of Ideals
Steven Dale Cutkosky, Juergen Herzog, Hema Srinivasan
TL;DR
This paper investigates the growth and finite generation of graded rings associated with symbolic powers and form ideals of powers of ideals, comparing them to ordinary powers in algebraic structures.
Contribution
It provides new insights into when the graded rings related to symbolic powers and form ideals are finitely generated, extending understanding of algebraic growth behaviors.
Findings
Comparison of growth rates between symbolic powers and ordinary powers
Conditions for finite generation of associated graded rings
Insights into algebraic structures related to ideal powers
Abstract
We study generalized symbolic powers and form ideals of powers of ideals and compare their growth with the growth of ordinary powers, and we discuss the question of when the graded rings attached to symbolic powers or to form ideals of powers are finitely generated.
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