7 papers · 1 filter
Symbolic powers and integral closures via extremal ideals
Trung Chau, Art Duval, Sara Faridi +3
This paper demonstrates that extremal ideals can be used to great effect to compute integral closures of powers and symbolic powers of square-free monomial ideals. We show that the…
Divisibility Relations and -Extremal ideals
Susan M. Cooper, Sabine El Khoury, Sara Faridi +3
A divisibility relation between the generators of a square-free monomial ideal formally encodes the situation when one generator divides the least common multiple of some other gen…
Simplicial Resolutions of the Quadratic Power of Monomial Ideals
Susan M. Cooper, Sara Faridi, Hasan Mahmood
Given any monomial ideal minimally generated by monomials, we define a simplicial complex that supports a resolution of . We also define a subco…
When are Morse resolutions polyhedral?
Louis Bu, Sara Faridi, Iresha Madduwe Hewalage +5
It is known that the chain complex of a simplex on vertices can be used to construct a free resolution of any ideal generated by monomials, and as a direct result, the Bett…
Artinian Gorenstein algebras with binomial Macaulay dual generator
Nasrin Altafi, Rodica Dinu, Sara Faridi +4
This paper initiates a systematic study for key properties of Artinian Gorenstein \(K\)-algebras having binomial Macaulay dual generators. In codimension 3, we demonstrate that all…
Realizing resolutions of powers of extremal ideals
Trung Chau, Art M. Duval, Sara Faridi +3
Extremal ideals are a class of square-free monomial ideals which dominate and determine many algebraic invariants of powers of all square-free monomial ideals. For example, the $r^…