Polarizations of powers of graded maximal ideals

Symbolic powers of generalized star configurations of hypersurfaces

“…Thus, τ ′ (g) = g 1 f for some squarefree monomial g 1 . Since τ ′ (g) ∈ J ≤k−1 , g 1 ∈ J ≤k−1 : f = G f , which was described in the above equation (1). Now the containment "⊆" follows from the S s actions.…”

“…Let Λ(J) := { λ(f ) : f ∈ G(J) } be the set of partitions of the minimal monomial generators of J. Without loss of generality, we may assume that Λ(J) = {λ (1) , . .…”

“…Here, ≺ is the total order we introduced in the proof of Theorem 2.6. For each k with 1 ≤ k ≤ t, let J ≤k ⊆ J be the sparse symmetric shifted ideal with Λ(J ≤k ) = {λ (1) , . .…”

“…For a fixed choice of positive integers a and b such that a ≤ bs, the generalized star configuration ideal that we shall study here is the uniform a-fold product ideal I a (F b ) := I a (f b 1 • • • f b s ). In general, the a-fold product ideal I a (f b 1 1 • • • f bs s ) is generated by the a-fold products of the forms f 1 , . .…”

Triangulations of polygons and stacked simplicial complexes: separating their Stanley–Reisner ideals

“…2. The ideal I (T ) is generated by the ten monomials The ideals I (T ) are introduced in [2] where they are shown to be all possible polarizations of the square of the graded maximal ideal (x e ) 2 e∈E in k[x e ] e∈E . If I X is the Stanley-Reisner ring of a stacked simplicial complex, we therefore have processes:…”