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
On the Relation Type of Fiber Cone
A. V. Jayanthan
,
Ramakrishna Nanduri
Abstract
In this article we study the relation type of the fiber cone of certain special classes of ideals in Noetherian local rings. We show that in any Noetherian local ring, if deviation of $I$ is $1$, and $\mathrm{depth}(G(\mathcal F_L)) \geq \ell-1$, then the relation types of $\mathcal R(I)$ and $F_L(I)$ are equal. We also prove that for lexsegment ideals in $K[x,y]$, where $K$ is a field, the relation types of the fiber cone and the Rees algebra are equal.