We investigate the Poisson algebras, in which n-th hypercenter (center) has a finite codimension. It was established that, this case, algebra P includes finite-dimensional ideal K such that P/K is nilpotent (Abelian). Moreover, if of over some field codimension, and does not contain zero divisors, then Abelian.

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.