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Journal Article
Locally Nilpotent Derivations of Graded Integral Domains and Cylindricity
2024
Overview
Let
B
be a commutative
ℤ
-graded domain of characteristic zero. An element
f
of
B
is said to be
cylindrical
if it is nonzero, homogeneous of nonzero degree, and such that
B
(
f
)
is a polynomial ring in one variable over a subring. We study the relation between the existence of a cylindrical element of
B
and the existence of a nonzero locally nilpotent derivation of
B
. Also, given
d
≥ 1, we give sufficient conditions that guarantee that every derivation of
B
(
d
)
=
⊕
i
∈
ℤ
B
d
i
can be extended to a derivation of
B
. We generalize some results of Kishimoto, Prokhorov and Zaidenberg that relate the cylindricity of a polarized projective variety (
Y
,
H
) to the existence of a nontrivial
G
a
-action on the affine cone over (
Y
,
H
).
Publisher
Springer US,Springer Nature B.V
Subject
