2010/10/13 by Ata Firat Pi̇r, Pir, Ata Fırat, Müfi̇t Sezer +1
Mathematics · #13F20 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.1010.2767
openalex publication_date 2010/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A homogeneous set of monomials in a quotient of the polynomial ring S:=F[x1, \..., xn] is called Gotzmann if the size of this set grows minimally when multiplied with the variables. We note that Gotzmann sets in the quotient R:=F[x1, \..., xn]/(x1a) arise from certain Gotzmann sets in S. Then we partition the monomials in a Gotzmann set in S with respect to the multiplicity of xi and show that if the growth of the size of a component is larger than the size of a neighboring component, then this component is a multiple of a Gotzmann set in F[x1, \..., xi-1, xi+1, \...,xn]. We also adopt some properties of the minimal growth of the Hilbert function in S to R.