Generic ideals and Moreno-Soc'ıas conjecture

2001/04/04 by Edith Aguirre, Abdul Salam Jarrah, Aguirre, Edith +7
Computer Science · Mathematics · #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.AC #math.RA

paper · pdf · doi:10.48550/arxiv.math/0104047

6 pages, 1 figure

arxiv created 2001/04/04 · openalex publication_date 2001/04/04 · arxiv updated 2009/11/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

Let f₁, ..., f_n be homogeneous polynomials generating a generic ideal I in the ring of polynomials in n variables over an infinite field. Moreno-Socías conjectured that for the graded reverse lexicographic term ordering, the initial ideal \rm in(I) is a weakly reverse lexicographic ideal. This paper contains a new proof of Moreno-Soc'ıas' conjecture for the case n=2.

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