Lovász–Saks–Schrijver ideals and coordinate sections of determinantal varieties

Krs and Determinantal Ideals

Krs and Determinantal Ideals

Quantum Determinantal Ideals

Introduction. Fix a base field k. The quantized coordinate ring of n×n matrices over k, denoted by q(Mn(k)), is a deformation of the classical coordinate ring of n×n matrices, (Mn(k)). As such, it is a k-algebra generated by n2 indeterminates Xij , for 1 ≤ i,j ≤ n, subject to relations which we state in (1.1). Here, q is a nonzero element of the field k. When q = 1, we recover (Mn(k)), which is...

Resultants of determinantal varieties

In this paper, a new kind of resultant, called the determinantal resultant, is introduced. This operator computes the projection of a determinantal variety under suitable hypothesis. As a direct generalization of the resultant of a very ample vector bundle [GKZ94], it corresponds to a necessary and sufficient condition so that a given morphism between two vector bundles on a projective variety ...

Krs and Powers of Determinantal Ideals

The goal of this paper is to determine Gröbner bases of powers of determinantal ideals and to show that the Rees algebras of (products of) determinantal ideals are normal and CohenMacaulay if the characteristic of the base field is non-exceptional. Our main combinatorial result is a generalization of Schensted’s Theorem on the Knuth–Robinson–Schensted correspondence. Mathematics Subject Classif...