5 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…
From points to complexes: a concept of unexpectedness for simplicial complexes
Thiago Holleben
In 2018, Cook, Harbourne, Migliore and Nagel introduced the concept of unexpected hypersurfaces, which connects the study of Lefschetz properties of artinian algebras defined by po…
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…
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^…
Coinvariant stresses, Lefschetz properties and random complexes
Thiago Holleben
Lefschetz properties and inverse systems have played key roles in understanding the -vector of simplicial spheres. In 1996, Lee established connections between these two algebra…