The degree sequence of ideals and multiplicities

2015/03/10 by Duong Quôc Việt, Viet, Duong Quoc
Computer Science · Mathematics · #13C15 #13D40 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 13H15 #Rings, Modules, and Algebras #Secondary 14C17

paper · pdf · doi:10.48550/arxiv.1503.02755

openalex publication_date 2015/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On Two Results of Mixed Multiplicities

Related

• A formula for the multiplicity of the multi-graded extended Rees algebra
• Computing epsilon multiplicities in graded algebras
• Mixed Multiplicities of Multi-Graded Algebras Over Noetherian Local Rings
• On multiplicities of graded sequences of ideals
• On the Upper bound of the Multiplicity Conjecture