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Triangulations of polygons and stacked simplicial complexes: separating their Stanley–Reisner ideals
A triangulation of a polygon has an associated Stanley–Reisner ideal. We obtain a full algebraic and combinatorial understanding of these ideals and...
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Stanley-Reisner Rings
This article is a try to describe the algebraic side of the story on Stanley-Reisner rings.
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On the Purity of Resolutions of Stanley-Reisner Rings Associated to Reed-Muller Codes
Following Johnsen and Verdure (2013), we can associate to any linear code C an abstract simplicial complex and in turn, a Stanley-Reisner ring...
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Which Properties of Stanley–Reisner Rings and Simplicial Complexes are Topological?
In this article we survey results on topological properties of simplicial complexes Δ, mostly defined via algebraic properties of its Stanley-Reisner...
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Hilbert series and suspensions of graphs
We explore the relationship between the Hilbert series of the edge ideal I of a graph and the combinatorial invariants of the graph, with a focus on...
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Frobenius methods in combinatorics
We survey results produced from the interaction between methods in prime characteristic and combinatorial commutative algebra. We showcase results...
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Duality in Toric Topology
We characterise integral Poincaré duality moment-angle complexes...
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The generic anisotropy of simplicial 1-spheres
The concept of generic anisotropy of a simplicial sphere was introduced by the authors as a key ingredient for a second proof of McMullen’s...
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Dga Models for Moment-Angle Complexes
A dga model for the integral singular cochains on a moment-angle complex is given by the twisted tensor product of the corresponding Stanley–Reisner...
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Graded Betti Numbers of Balanced Simplicial Complexes
We prove upper bounds for the graded Betti numbers of Stanley-Reisner rings of balanced simplicial complexes. Along the way we show bounds for...
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Cohomology Rings of Toric Bundles and the Ring of Conditions
The celebrated BKK Theorem expresses the number of roots of a system of generic Laurent polynomials in terms of the mixed volume of the corresponding...
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Frobenius and Cartier Algebras of Stanley–Reisner Rings (II)
It is known that the Frobenius algebra of the injective hull of the residue field of a complete Stanley–Reisner ring (i.e., a formal power series...
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Generalized Virtual Polytopes and Quasitoric Manifolds
AbstractWe develop a theory of volume polynomials of generalized virtual polytopes based on the study of topology of affine subspace arrangements in...
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4-Dimensional Licci Gorenstein Stanley-Reisner Ideals
We classify licci Gorenstein squarefree monomial ideals I with dim S / I ≤ 4, where S is a polynomial ring.