相关论文: Hilbert Regularity of Stanley-Reisner Rings

Let $\Delta$ be simplicial complex and let $k[\Delta]$ denote the Stanley--Reisner ring corresponding to $\Delta$. Suppose that $k[\Delta]$ has a pure free resolution. Then we describe the Betti numbers and the Hilbert--Samuel multiplicity…

Let $\Delta$ be simplicial complex and let $k[\Delta]$ denote the Stanley--Reisner ring corresponding to $\Delta$. Suppose that $k[\Delta]$ has a pure free resolution. Then we describe the Betti numbers and the Hilbert--Samuel multiplicity…

We investigate generalized notions of the nerve complex for the facets of a simplicial complex. We show that the homologies of these higher nerve complexes determine the depth of the Stanley-Reisner ring $k[\Delta]$ as well as the…

Given an infinite field $\mathbb{k}$ and a simplicial complex $\Delta$, a common theme in studying the $f$- and $h$-vectors of $\Delta$ has been the consideration of the Hilbert series of the Stanley--Reisner ring $\mathbb{k}[\Delta]$…

We study the regularity and the projective dimension of the Stanley-Reisner ring of a $k$-decomposable simplicial complex and explain these invariants with a recursive formula. To this aim, the graded Betti numbers of $k$-decomposable…

When $I$ is the edge ideal of a graph $G$, we use combinatorial properities, particularly Property $P$ on connectivity of neighbors of an edge, to classify when a binomial sum of vertices is a regular element on $R/I(G)$. Under a mild…

We characterize all Gorenstein rings generated by strongly stable sets of monomials of degree two. We compute their Hilbert series in several cases, which also provides an answer to a question by Migliore and Nagel.

We give an explicit formula for the Hilbert Series of an algebra defined by a linearly presented, standard graded, residual intersection of a grade three Gorenstein ideal.

We describe the graded characters and Hilbert functions of certain graded artinian Gorenstein quotients of the polynomial ring which are also representations of the symmetric group. Specifically, we look at those algebras whose socles are…

We study the exponential Hilbert series (both coarsely- and finely-graded) of the Stanley-Reisner ring of an abstract simplicial complex, $\Delta$, and we introduce the $e$-vector of $\Delta$, which relates to the coefficients of the…

Let $R$ be a local ring of characteristic $p>0$ which is $F$-finite and has perfect residue field. We compute the generalized Hilbert-Kunz invariant for certain modules over several classes of rings: hypersurfaces of finite representation…

In this paper, we estimate the Hilbert-Kunz multiplicity of the (extended) Rees algebras in terms of some invariants of the base ring. Also, we give an explicit formula for the Hilbert-Kunz multiplicities of Rees algebras over Veronese…

For a simplicial complex $\Delta$ we study the effect of barycentric subdivision on ring theoretic invariants of its Stanley-Reisner ring. In particular, for Stanley-Reisner rings of barycentric subdivisions we verify a conjecture by Huneke…

The Hilbert functions and the regularity of the graded components of local cohomology of a bigraded algebra are considered. Explicit bounds for these invariants are obtained for bigraded hypersurface rings.

We describe the category of regular holonomic modules over the ring D[[h]] of linear differential operators with a formal parameter h. In particular, we establish the Riemann-Hilbert correspondence and discuss the additional t-structure…

We give a bound for the Betti numbers of the Stanley-Reisner ring of a stellar subdivision of a Gorenstein* simplicial complex by applying unprojection theory. From this we derive a bound for the Betti numbers of iterated stellar…

We study the regularity of minima of scalar variational integrals of $p$-growth, $1<p<\infty$, in the Heisenberg group.

We study the regularity of minima of scalar variational integrals of $p$-growth, $1<p<\infty$, in the Heisenberg group and prove the H\"older continuity of horizontal gradient of minima.

Given a classical symmetric pair, $(G,K)$, with $\mathfrak g = Lie(G)$, we provide descriptions of the Hilbert series of the algebra of $K$-invariant vectors in the associated graded algebra of $\mathcal U(\mathfrak g)$ viewed as a…

We compute the regularity of the Hibi ring of any finite distributive lattice in terms of its poset of join irreducible elements.