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Abstract
The Cohen-Macaulay condition is added to the statements of Proposition 3.3 and Corollary 3.4. We also correct some small typos.
Raheleh Jafaria, Abdoljavad Taherizadehb, Marjan Yaghmaeib
aMosaheb Institute of Mathematics, Kharazmi University,Tehran, Iran
bFaculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
CONTACT Raheleh Jafari [email protected] Mosaheb Institute of Mathematics, Kharazmi University, Tehran, Iran.
In proposition 3.3, for the implication (2) (1), we use Theorem 3.1 where we need
to be Cohen-Macaulay. Thus, we need the Cohen-Macaulay assumption in Proposition 3.3 and Corollary 3.4, as well.
Proposition 3.3
Let be the dimension of the non-Gorenestein locus of
. If
is Cohen-Macaulay, then the following statements are equivalent for an integer
.
.
For any face F of S such that
has k + 1 elements, there exists
and
such that
for all
.
Corollary 3.4
If is Cohen-Macaulay, then
is Gorenstein on the punctured spectrum precisely when, for any , there e
xist
and
such that
for all
.
On the 3rd line of the preliminaries section, the phrase should be
.
In the proof of Corollary 3.4, “Proposition 3.3” should be “Corollary 3.3”.
On the 3rd line of the proof of Corollary 3.5, the correct equation is