On the isomorphisms of smooth algebraic curves

Abstract

In this paper, I have considered some problems of algebraic curves in some constructive way, especially, I give an algorithm for determining whether two given smooth plane curves are isomorphic and finding all isomorphic maps. I also have given a survey of some miscellaneous results related to the classification of curves. In the appendix, I give some other results which implies a more efficient algorithm for deciding whether two plane curves are isomorphic and finding all isomorphic maps. It is clear our method in this paper can be generalized to smooth projective complete intersection varieties.