Let R be an algebra essentially of finite type over a field k and let Ω k pRq be its module of Kähler differentials over k. If R is a homogeneous complete intersection and charpkq " 0, we prove that Ω k pRq is of linear type whenever its Rees algebra is Cohen-Macaulay and locally at every homogeneous prime p the embedding dimension of Rp is at most twice its dimension.
Let
R
R
be an algebra essentially of finite type over a field
k
k
and let
Ω
k
(
R
)
\Omega _k(R)
be its module of Kähler differentials over
k
k
. If
R
R
is a homogeneous complete intersection and
c
h
a
r
(
k
)
=
0
\mathrm {char}(k)=0
, we prove that
Ω
k
(
R
)
\Omega _k(R)
is of linear type whenever its Rees algebra is Cohen-Macaulay and locally at every non-maximal homogeneous prime
p
\mathfrak {p}
the embedding dimension of
R
p
R_{\mathfrak {p}}
is at most twice its dimension. This improves a previous result of Simis, Ulrich and Vasconcelos for the module of differentials of a ring that is locally a complete intersection, in which case the latter condition is assumed locally at every prime.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.