Geodesic
Algebraic curves with an infinite automorphism group
Matematičeskie zametki, Tome 23 (1978) no. 2, pp. 183-195.

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Irreducible algebraic curves $X$ (not necessarily smooth and complete) for which the group $\operatorname{Aut}X$ of biregular automorphisms is infinite are classified. Applications of the results obtained to the theory of algebraic transformation groups are given. 
@article{MZM_1978_23_2_a1,
     author = {V. L. Popov},
     title = {Algebraic curves with an infinite automorphism group},
     journal = {Matemati\v{c}eskie zametki},
     pages = {183--195},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_2_a1/}
}
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V. L. Popov. Algebraic curves with an infinite automorphism group. Matematičeskie zametki, Tome 23 (1978) no. 2, pp. 183-195. http://geodesic.mathdoc.fr/item/MZM_1978_23_2_a1/