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Depth of powers of edge ideals of Cohen-Macaulay trees
Authors
Nguyen Thu Hang
Truong Thi Hien
Thanh Vu
Publication date
10 September 2023
Publisher
View
on
arXiv
Abstract
Let
I
I
I
be the edge ideal of a Cohen-Macaulay tree of dimension
d
d
d
over a polynomial ring
S
=
k
[
x
1
,
β¦
,
x
d
,
y
1
,
β¦
,
y
d
]
S = \mathrm{k}[x_1,\ldots,x_{d},y_1,\ldots,y_d]
S
=
k
[
x
1
β
,
β¦
,
x
d
β
,
y
1
β
,
β¦
,
y
d
β
]
. We prove that for all
t
β₯
1
t \ge 1
t
β₯
1
,
\operatorname{depth} (S/I^t) = \operatorname{max} \{d -t + 1, 1 \}.$
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oai:arXiv.org:2309.05011
Last time updated on 06/10/2023