On Hilbert polynomial of certain determinantal ideals

Hilbert Polynomial of a Certain Ladder-Determinantal Ideal

A ladder-shaped array is a subset of a rectangular array which looks like a Ferrers diagram corresponding to a partition of a positive integer. The ideals generated by the p-by-p minors of a ladder-type array of indeterminates in the corresponding polynomial ring have been shown to be hilbertian (i.e., their Hilbert functions coincide with Hilbert polynomials for all nonnegative integers) by Ab...

Prime Ideals in Certain Quantum Determinantal Rings

The ideal I 1 generated by the 2 2 quantum minors in the coordinate algebra of quantum matrices, O q (M m;n (k)), is investigated. Analogues of the First and Second Fundamental Theorems of Invariant Theory are proved. In particular, it is shown that I 1 is a completely prime ideal, that is, O q (M m;n (k))=I 1 is an integral domain, and that O q (M m;n (k))=I 1 is the ring of coinvariants of a ...

Hilbert Series of Certain Jet Schemes of Determinantal Varieties

We consider the affine variety Z 2,2 of first order jets over Z m,n 2 , where Z 2 is the classical determinantal variety given by the vanishing of all 2×2 minors of a generic m×n matrix. When 2 < m ≤ n, this jet scheme Z 2,2 has two irreducible components: a trivial component, isomorphic to an affine space, and a nontrivial component that is the closure of the jets supported over the smooth loc...

Krs and Determinantal Ideals

Krs and Determinantal Ideals