On Borel fixed ideals generated in one degree

2007/02/22 by Sinefakopoulos, Achilleas
#13F20 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0702629

Abstract

We construct a (shellable) polyhedral cell complex that supports a minimal free resolution of a Borel fixed ideal, which is minimally generated (in the Borel sense) by just one monomial in S=k[x₁,x₂,...,x_n]; this includes the case of powers of the homogeneous maximal ideal (x₁,x₂,...,x_n) as a special case. In our most general result we prove that for any Borel fixed ideal I generated in one degree, there exists a polyhedral cell complex that supports a minimal free resolution of I.

Related

• Powers of graphs & applications to resolutions of powers of monomial ideals
• Cellular resolutions of monomial ideals and their Artinian reductions
• When are Morse resolutions polyhedral?
• Resolutions of square-free monomial ideals via facet ideals: a survey
• A Minimal Poset Resolution of Stable Ideals