Let G be a simple undirected graph on n vertices, and let I(G) ⊆ R = k[x 1 ,. .. , x n ] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that the Alexander dual of I(G) is componentwise linear. Our result complements Faridi's theorem that the facet ideal of a simplicial tree is sequentially Cohen-Macaulay and He...

We study properties of a poset generating a Cohen-Macaulay algebra with straightening laws (ASL for short). We show that if a poset P generates a Cohen-Macaulay ASL, then P is pure and, if P is moreover Buchsbaum, then P is Cohen-Macaulay. Some results concerning a Rees algebra of an ASL defined by a straightening closed ideal are also established. And it is shown that if P is a Cohen-Macaulay ...

Given a local Noetherian ring (R, m) of dimension d > 0 and infinite residue field, we study the invariants (dimension and multiplicity) of the Sally module SJ (I) of any m-primary ideal I with respect to a minimal reduction J. As a by-product we obtain an estimate for the Hilbert coefficients of m that generalizes a bound established by J. Elias and G. Valla in a local Cohen-Macaulay setting. ...

We analyze the behavior of the holonomic rank in families of holonomicsystems over complex algebraic varieties by providing homological criteria for rank-jumpsin this general setting. Then we investigate rank-jump behavior for hypergeometric sys-tems HA(β) arising from a d × n integer matrix A and a parameter β ∈ C. To doso we introduce an Euler–Koszul functor for hypergeometric...

Let G be a simple undirected graph on n vertices, and let I(G) ⊆ R = k[x1, . . . , xn] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that the Alexander dual of I(G) is componentwise linear. Our result complements Faridi’s theorem that the facet ideal of a simplicial tree is sequentially Cohen-Macaulay and impl...

A commutative local Cohen-Macaulay ring R of finite Cohen-Macaulay type is known to be an isolated singularity; that is, Spec(R) \ {m} is smooth. This paper proves a non-commutative analogue. Namely, if A is a (non-commutative) graded Artin-Schelter Cohen-Macaulay algebra which is FBN and has finite Cohen-Macaulay type, then the non-commutative projective scheme determined by A is smooth.