Rank Jumps in Codimension

Rank Jumps in Codimension 2A-hypergeometric Systems

The holonomic rank of the A-hypergeometric system HA(β) is shown to depend on the parameter vector β when the underlying toric ideal IA is a non Cohen Macaulay codimension 2 toric ideal. The set of exceptional parameters is usually infinite.

Lifting Problem in Codimension 2 and Initial Ideals

APPROXIMATE IDENTITY IN CLOSED CODIMENSION ONE IDEALS OF SEMIGROUP ALGEBRAS

Let S be a locally compact topological foundation semigroup with identity and Ma(S) be its semigroup algebra. In this paper, we give necessary and sufficient conditions to have abounded approximate identity in closed codimension one ideals of the semigroup algebra $M_a(S)$ of a locally compact topological foundationsemigroup with identity.

Cohen-Macaulay-ness in codimension for simplicial complexes and expansion functor

In this paper we show that expansion of a Buchsbaum simplicial complex is $CM_t$, for an optimal integer $tgeq 1$. Also, by imposing extra assumptions on a $CM_t$ simplicial complex, we provethat it can be obtained from a Buchsbaum complex.

Degrees of High-dimensional Subvarieties of Determinantal Varieties

Let n = pab, where p is a prime, and g.c.d.(p, b) = 1. In Pn −1, let Xr be the variety defined by rank((xi,j)) ≤ n − r. We show that any subvariety of Xr of codimension less than par must have degree a multiple of p. We also show that the bounds on the codimension in our results are strict by exhibiting subvarieties of the appropriate codimension whose degrees are