13 papers
Cellular resolutions of second powers of square-free monomial ideals with divisibility relations
Susan M. Cooper, Sabine El Khoury, Sara Faridi +3
Using divisibility relations between the generators of a square-free monomial ideal , we describe divisibility relations between the generators of the second power . We the…
Cohen-Macaulay squares of edge ideals
Sara Faridi, Takayuki Hibi
Let be a finite graph and its edge ideal. We give a full description of the Stanley--Reisner complex of the polarization of , naturally introducing the tools of…
Scarf complexes of graphs and their powers
Sara Faridi, TÃ i Huy HÃ, Takayuki Hibi +1
Every multigraded free resolution of a monomial ideal I contains the Scarf multidegrees of I. We say I has a Scarf resolution if the Scarf multidegrees are sufficient to describe a…
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…
Polarization and Gorenstein liaison
Sara Faridi, Patricia Klein, Jenna Rajchgot +1
A major open question in the theory of Gorenstein liaison is whether or not every arithmetically Cohen--Macaulay subscheme of can be G-linked to a complete intersect…
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…