Acta Mathematica Vietnamica
- Volume 49
- Volume 48
- Volume 47
- Volume 46
- Volume 45
- Volume 44
- Volume 43
- Volume 42
- Volume 41
- Volume 40
- Volume 39
- Volume 38
- Volume 37
- Volume 36
- Volume 35
- Volume 34
- Volume 33
- Volume 32
- Volume 31
- Volume 30
- Volume 29
- Volume 28
- Volume 27
- Volume 26
- Volume 25
- Volume 24
- Volume 23
- Volume 22
- Volume 21
- Volume 20
- Volume 19
- Volume 18
- Volume 17
- Volume 16
- Volume 15
- Volume 14
- Volume 13
- Volume 12
- Volume 11
- Volume 10
- Volume 9
- Volume 8
- Volume 7
- Volume 6
- Volume 5
- Volume 4
- Volume 3
- Volume 2
- Volume 1
Stability of Depth and Cohen-Macaulayness of Integral Closures of Powers of Monomial Ideals
Le Tuan Hoa
,
Tran Nam Trung
Abstract
Let $I$ be a monomial ideal in a polynomial ring $R = k[x_{1},\dots ,x_{r}]$. In this paper, we give an upper bound on $\overline {\text {dstab}} (I)$ in terms of $r$ and the maximal generating degree $d(I)$ of $I$ such that $\text {depth} R/\overline {I^{n}}$ is constant for all $n\geqslant \overline {\text {dstab}}(I)$. As an application, we classify the class of monomial ideals $I$ such that $\overline {I^{n}}$ is Cohen-Macaulay for some integer $n\gg 0$.