2006/02/22 by Giulio Caviglia, Caviglia, Giulio
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #13P10 #16S37 #Biological Activity of Diterpenoids and Biflavonoids #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.CO #msc:13P10 #msc:16S37
paper · pdf · doi:10.48550/arxiv.math/0602487
8 Pages
arxiv created 2006/02/22 · openalex publication_date 2006/02/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove that the coordinate ring of the pinched Veronese (i.e k[X3,X2Y,XY2,Y3,X2Z,Y2Z,XZ2,YZ2,Z3]⊂ k[X,Y,Z]) is Koszul. The strategy of the proof is the following: we can consider a presentation S/I where S=k[X1,...,X9]. Using a distinguished weight ω, it's enough to show that S/inωI is Koszul. We write inωI as J+H where J is generated by a Gröbner basis of quadrics. Finally, we present an extension of the notion of Koszul filtration and we use it to show that (J+H)/J has a linear free resolution over S/J. This implies the Koszulness of S/I.