Let K be a field with char(K)=0. For partition λ of n∈N, let IλSp the ideal R=K[x1,…,xn] generated by all Specht polynomials shape λ. These ideals have been studied from several points view (and under names). Using advanced tools representation theory, Berkesch Zamaere et al. [1] constructed minimal free resolution I(n−d,d)Sp except differential maps. The present paper constructs maps, and also...

Let U ⊆ H(OP1×P1 (2, 1)) be a basepoint free four-dimensional vector space. The sections corresponding to U determine a regular map φU : P1 × P1 −→ P3. We study the associated bigraded ideal IU ⊆ k[s, t;u, v] from the standpoint of commutative algebra, proving that there are exactly six numerical types of possible bigraded minimal free resolution. These resolutions play a key role in determinin...

We define the reduced horseshoe resolution and the notion of conjoined pairs of ideals in order to study the minimal graded free resolution of a class of p-Borel ideals and recover Pardue’s regularity formula for them. It will follow from our technique that the graded betti numbers of these ideals do not depend on the characteristic of the base field k.

Hochster established the existence of a commutative noetherian ring R and a universal resolution U of the form 0 ! R ! R ! R ! 0 such that for any commutative noetherian ring S and any resolution V equal to 0! S ! S ! S g ! 0, there exists a unique ring homomorphism R ! S with V = U R S. In the present paper we assume that f = e + g and we nd a resolution of R by free P-modules, where P is a po...

The automorphism group of a curve is studied from the viewpoint canonical embedding and Petri’s theorem. A criterion for identifying as an algebraic subgroup general linear given. Furthermore, action extended to on generators minimal free resolution ring X.

For a finitely generated submonoid Λ of N, we consider the minimal free resolution of a field k as a module over the monoid algebra k[Λ]. Interpreting the ranks of the free modules in the resolution as the homology of certain simplicial complexes associated to posets, we show how non-commutative Gröbner bases and the non-pure shellings of Björner and Wachs can be used to obtain information abou...