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Incidence toric ideals and three-point functions
Barbara Betti, Sean Grate, Thiago Holleben +1
We study the ideal of the algebraic relations among 3-point functions from a combinatorial and topological perspective. We place this problem in the broader setting of incidence to…
Weighted Veronese Rings via Convex Semigroups
Bek Chase, Luca Fiorindo, Thiago Holleben +4
We determine properties of two-dimensional normal affine semigroup rings, and in particular of weighted Veronese rings, including determinantal presentation, Gröbner basis, graded…
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…
Roller Coaster Gorenstein algebras and Koszul algebras failing the weak Lefschetz property
Thiago Holleben, Lisa Nicklasson
Inspired by the Roller Coaster Theorem from graph theory, we prove the existence of artinian Gorenstein algebras with unconstrained Hilbert series, which we call Roller Coaster alg…
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…
Lefschetz properties of squarefree monomial ideals via Rees algebras
Thiago Holleben
The theory of Rees algebras of monomial ideals has been extensively studied, and as a consequence, many (sometimes partial) equivalences between algebraic properties of monomial id…
Spherical complexes
Sara Faridi, Thiago Holleben
In this paper we define spherical complexes as simplicial complexes with the property that every subcomplex obtained by a sequence of links and deletions either has trivial homolog…
The weak Lefschetz property and mixed multiplicities of monomial ideals
Thiago Holleben
Recently, H. Dao and R. Nair gave a combinatorial description of simplicial complexes such that the squarefree reduction of the Stanley-Reisner ideal of has the WLP in degr…
The weak Lefschetz property of whiskered graphs
Susan M. Cooper, Sara Faridi, Thiago Holleben +2
We consider Artinian level algebras arising from the whiskering of a graph. Employing a result by Dao-Nair we show that multiplication by a general linear form has maximal rank in…