The cleanness of (symbolic) powers of Stanley-Reisner ideals

Bandari, Somayeh; Jahan, Ali Soleyman

doi:10.21136/cmj.2017.0173-16

Search citation statements

Order By: Relevance

Paper Sections

Select...

Depth Of Symbolic Powers1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2019

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…x αn n . Takayama [19, Theorem 2.2] proves that for any vector α ∈ Z n and for every integer i, we have (1) dim…”

Section: Depth Of Symbolic Powersmentioning

confidence: 99%

Stability of depth and Stanley depth of symbolic powers of squarefree monomial ideals

Fakhari

2019

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

Let K be a field and S = K[x 1 , . . . , x n ] be the polynomial ring in n variables over K. Assume that I ⊂ S is a squarefree monomial ideal. For every integer k ≥ 1, we denote the k-th symbolic power of I by I (k) . Recently, Montaño and Núñez-Betancourt [14] proved that for every pair of integers m, k ≥ 1,). We provide an alternative proof for this inequality. Moreover, we reprove the known results that the sequence {depth(S/I (k) )} ∞ k=1 is convergent and min k depth(S/I (k) ) = lim k→∞ depth(S/I (k) ) = n − ℓ s (I),where ℓ s (I) denotes the symbolic analytic spread of I. We also determine an upper bound for the index of depth stability of symbolic powers of I. Next, we consider the Stanley depth of symbolic powers and prove that the sequences {sdepth(S/I (k) )} ∞ k=1 and {sdepth(I (k) )} ∞ k=1 are convergent and the limit of each sequence is equal to its minimum. Furthermore, we determine an upper bound for the indices of sdepth stability of symbolic powers.

show abstract

“…x αn n . Takayama [19, Theorem 2.2] proves that for any vector α ∈ Z n and for every integer i, we have (1) dim…”

Section: Depth Of Symbolic Powersmentioning

confidence: 99%