Canonical Hilbert-Burch matrices for ideals of k[x,y]

2007/08/27 by Aldo Conca, Conca, Aldo, Giuseppe Valla +1
Mathematics · #13P10 #14C05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13P10 #msc:14C05

paper · pdf · doi:10.48550/arxiv.0708.3576

arxiv created 2007/08/27 · arxiv updated 2009/12/01

Abstract

An Artinian ideal I of k[x,y] has many Hilbert-Burch matrices. We show that there is a canonical choice. As an application, we determine the dimension of certain affine Gröbner cells and their Betti strata recovering results of Ellingsrud and Strømme, Göttsche and Iarrobino.

Related

• Canonical Hilbert-Burch matrices for power series
• Deformations of local Artin rings via Hilbert-Burch matrices
• Linearly presented perfect ideals of codimension 2 in three variables
• On Rees algebras of linearly presented ideals and modules
• Hilbert-Burch matrices and explicit torus-stable families of finite subschemes of \mathbb A ²