Betti numbers of monomial ideals in four variables

2019/05/03 by Alesandroni, Guillermo
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.01151

Abstract

We express the multigraded Betti numbers of monomial ideals in 4 variables in terms of the multigraded Betti numbers of 66 squarefree monomial ideals, also in 4 variables. We use this class of 66 ideals to prove that monomial resolutions in 4 variables are independent of the base field. In addition, we give a formula for the Betti numbers of an arbitrary monomial ideal in 4 variables.

Related

• Structural decomposition of monomial resolutions
• Characteristic Independence of Betti Numbers of Monomial Ideals in Five Variables
• Monomial ideals with large projective dimension
• Betti numbers of monomial ideals and shifted skew shapes
• Building monomial ideals with fixed betti numbers