論文の公開元へProjective plane curves whose automorphism groups are simple and primitive
概要
Automorphism groups of algebraic curves have long been studied. For example,
Hurwitz found an upper bound on the order of the automorphism group of a curve
of a given genus ([6]). In the case of plane curves, there are more detailed studies
on automorphism groups. One important fact here is that an automorphism of a
smooth projective plane curve of degree greater than or equal to 4 uniquely extends
to an automorphism of the projective plane. Hence, the automorphism group of
such a curve is isomorphic to a subgroup of PGL(3, C).
Recently, Harui obtained the following result concerning the classification of
automorphism groups of smooth plane curves.
Theorem 1.1. ([4, Theorem 2.3]) Let C be a smooth plane curve of degree d ≥ 4,
and G a subgroup of Aut C. Then one of the following holds:
(a-i) G fixes a point on C, and G is cyclic. ...
