Earlier results expressing multivariate subresultants as ratios of two subdeterminants of the Macaulay matrix are extended to Jouanolou’s resultant matrices. These matrix constructions are generalizations of the classical Macaulay matrices and involve matrices of significantly smaller size. Equivalence of the various subresultant constructions is proved. The resulting subresultant method improv...

We study Stanley decompositions and show that Stanley’s conjecture on Stanley decompositions implies his conjecture on partitionable Cohen-Macaulay simplicial complexes. We also prove these conjectures for all Cohen-Macaulay monomial ideals of codimension 2 and all Gorenstein monomial ideals of codimension 3.

In this paper, we explore the relation between index of reducibility and Hilbert coefficients in local rings. Consequently, main result study provides a characterization sequentially Cohen-Macaulay ring terms its non-parameter ideals. As corollaries to theorem, obtain characterizations Gorenstein/Cohen-Macaulay Chern

We define a simplicial complex ∆ W in terms of polygon dissections for every classical reflection group W and positive integer m. For m = 1, ∆ W is isomorphic to the cluster complex corresponding to W , defined in [8]. We enumerate the faces of ∆ W and show that the entries of its h-vector are given by the generalized Narayana numbers N W (i), defined in [3]. We also prove that for any m ≥ 1 th...

This paper considers the problems of finite determinacy and approximation flat analytic maps from germs real (resp. complex) spaces to R </mml...

We study Stanley decompositions and show that Stanley’s conjecture on Stanley decompositions implies his conjecture on partitionable Cohen-Macaulay simplicial complexes. We also prove these conjectures for all Cohen-Macaulay monomial ideals of codimension 2 and all Gorenstein monomial ideals of codimension 3.

We show that monomial ideals generated in degree two satisfy a conjecture by Eisenbud, Green and Harris. In particular we give a partial answer to a conjecture of Kalai by proving that h-vectors of flag Cohen-Macaulay simplicial complexes are h-vectors of Cohen-Macaulay balanced simplicial complexes.

The goal of the present paper is study some algebraic invariants Stanley–Reisner rings Cohen–Macaulay simplicial complexes dimension d−1. We prove that inequality d≤reg(Δ)⋅type(Δ) holds for any (d−1)-dimensional complex Δ satisfying Δ=core(Δ), where reg(Δ) (resp. type(Δ)) denotes Castelnuovo–Mumford regularity type) ring k[Δ]. Moreover, given integers d,r,t r,t≥2 and r≤d≤rt, we construct a Δ(G)...

The type II1 unprojection is, by definition, the generic complete intersection type II unprojection, in the sense of [P] Section 3.1, for the parameter value k = 1, and depends on a parameter n ≥ 2. Our main results are the explicit calculation of the linear relations of the type II1 unprojection for any value n ≥ 2 (Theorem 3.16) and the explicit calculation of the quadratic equation for the c...

The theorem of Hochster and Roberts says that for any module V of a linearly reductive group G over a eld K the invariant ring KV ] G is Cohen-Macaulay. We prove the following converse: if G is a reductive group and KV ] G is Cohen-Macaulay for any module V , then G is linearly reductive.