For t in Nn, E.Miller has defined a category of t-determined modules over the polynomial ring S in n variables. We consider the Auslander-Reiten translate, Nt, on the (derived) category of such modules. A monomial ideal I is t-determined if every generator x has a ≤ t. We compute the multigraded cohomologyand betti spaces of N k t (S/I) for every iterate k, and also the Smodule structure of the...

We prove that the f -vector of members in a certain class of meet semi-lattices satisfies Macaulay inequalities 0 ≤ ∂k(fk) ≤ fk−1 for all k ≥ 0. We construct a large family of meet semi-lattices belonging to this class, which includes all posets of multicomplexes, as well as meet semi-lattices with the ”diamond property”, discussed by Wegner [11], as special cases. Specializing the proof to the...

Extending work of Bielawski-Dancer [3] and Konno [12], we develop a theory of toric hyperkähler varieties, which involves toric geometry, matroid theory and convex polyhedra. The framework is a detailed study of semi-projective toric varieties, meaning GIT quotients of affine spaces by torus actions, and specifically, of Lawrence toric varieties, meaning GIT quotients of even-dimensional affine...

This paper produces a recursive formula of the Betti numbers of certain StanleyReisner ideals (graph ideals associated to forests). This gives a purely combinatorial definition of the projective dimension of these ideals, which turns out to be a new numerical invariant of forests. Finally, we propose a possible extension of this invariant to general graphs. 0. Introduction Throughout this paper...

Following Johnsen and Verdure (2013), we can associate to any linear code $C$ an abstract simplicial complex in turn, a Stanley-Reisner ring $R_C$. The $R_C$ is standard graded algebra over field its projective dimension precisely the of $C$. Thus admits minimal free resolution resulting Betti numbers are known determine generalized Hamming weights question purity was considered by Ghorpade Sin...

In this paper, we prove that the Stanley–Reisner ideal of any connected simplicial complex of dimension ≥ 2 that is locally complete intersection is a complete intersection ideal. As an application, we show that the Stanley–Reisner ideal whose powers are Buchsbaum is a complete intersection ideal.

The goal of the present paper is study some algebraic invariants Stanley–Reisner rings Cohen–Macaulay simplicial complexes dimension d−1. We prove that inequality d≤reg(Δ)⋅type(Δ) holds for any (d−1)-dimensional complex Δ satisfying Δ=core(Δ), where reg(Δ) (resp. type(Δ)) denotes Castelnuovo–Mumford regularity type) ring k[Δ]. Moreover, given integers d,r,t r,t≥2 and r≤d≤rt, we construct a Δ(G)...

The antiprism triangulation provides a natural way to subdivide simplicial complex \(\Delta \), similar barycentric subdivision, which appeared independently in combinatorial algebraic topology and computer science. It can be defined as the of chains multi-pointed faces from point view, by successively applying construction, or balanced stellar subdivisions, on geometric view. This paper studie...

Given a simplicial complex, it is easy to construct a generic deformation of its Stanley-Reisner ideal. The main question under investigation in this paper is how to characterize the simplicial complexes such that their Stanley-Reisner ideals have Cohen-Macaulay generic deformations. Algorithms are presented to construct such deformations for matroid complexes, shifted complexes, and tree compl...