Stellar subdivisions and Stanley-Reisner rings of Gorenstein complexes

Connected Sums of Simplicial Complexes and Equivariant Cohomology

Abstract In this paper, we introduce the notion of a connected sum K1 #Z K2 of simplicial complexes K1 and K2, as well as define a strong connected sum. Geometrically, the connected sum is motivated by Lerman’s symplectic cut applied to a toric orbifold, and algebraically, it is motivated by the connected sum of rings introduced by Ananthnarayan–Avramov–Moore [1]. We show that the Stanley–Reisn...

On a special class of Stanley-Reisner ideals

For an $n$-gon with vertices at points $1,2,cdots,n$, the Betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. In this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and Betti numbers of the $S$-module $S/I$ where  $S=K[x_{1},cdots, x_{n}]$ and $I$ is the associated ideal to ...

On Isomorphism of Simplicial Complexes and Their Related Algebras

On Toric Face Rings

Following a construction of Stanley we consider toric face rings associated to rational pointed fans. This class of rings is a common generalization of the concepts of Stanley–Reisner and affine monoid algebras. The main goal of this article is to unify parts of the theories of Stanley–Reisnerand affine monoid algebras. We consider (nonpure) shellable fan’s and the Cohen–Macaulay property. More...

The Multiplicity Conjecture for Barycentric Subdivisions

For a simplicial complex ∆ we study the effect of barycentric subdivision on ring theoretic invariants of its StanleyReisner ring. In particular, for Stanley-Reisner rings of barycentric subdivisions we verify a conjecture by Huneke and Herzog & Srinivasan, that relates the multiplicity of a standard graded k-algebra to the product of the maximal shifts in its minimal free resolution up to the ...