The degree sequence of ideals and multiplicities
Duong Quoc Viet
TL;DR
This paper explores how the degree sequence of ideals in graded algebras relates to multiplicities, providing formulas and characterizations, and resolving an open question on Rees ring multiplicities.
Contribution
It introduces new relationships between multiplicities and degree sequences, and characterizes mixed and Rees ring multiplicities in terms of degree sequences.
Findings
Derived multiplicity equations for graded rings.
Characterized mixed multiplicities via degree sequences.
Answered an open question on Rees ring multiplicity.
Abstract
This paper investigates the relationship between multiplicities and the degree sequence of ideals in graded algebras, gives multiplicity equations of graded rings via the degree sequence of ideals, and characterizes mixed multiplicities and multiplicities of Rees rings in terms of the degree sequence of ideals. As an application, the paper answered an open question on the multiplicity of Rees rings.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Rings, Modules, and Algebras · Polynomial and algebraic computation