On the effective reduction of an ideal

2021/06/22 by Rodak, Tomasz, Różycki, Adam, Spodzieja, Stanisław
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2106.11648

Abstract

It is well known that in the Noetherian local ring with infinite residue field the reduction of \mm-primary ideal may be given in the form of a sufficiently general linear combination of its generators. In the paper we give a condition for the existence of such reduction in terms of the sum of degrees of the ideal fiber cone prime divisors in the case of any Noetherian local ring.

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• Generators of reductions of ideals in a local Noetherian ring with\n finite residue field
• Sally modules of \mathfrak m-primary ideals in local rings
• Ratliff-Rush ideal and reduction numbers
• Multiplicity of the special fiber of blowups
• Results on the Hilbert coefficients and reduction numbers