Study on the various structures of algebraic surfaces by Galois embeddings

假设阿贝尔曲面A有伽罗瓦嵌入。那么，使A嵌入到射影n空间中的最小n是多少？答案是7，而且这样的阿贝尔曲面与E×E同构，其中E是一条椭圆曲线。我们还考虑了曲线的问题。对于属为1的平面曲线，当它有伽罗瓦点时，我们发现它有伽罗瓦群；对于空间椭圆曲线，我们发现它总是有伽罗瓦线。

Suppose an abelian surface A has a Galois embedding. Then, what is the least number n such that A is embedded into the projective n-space? The answer is 7 and moreover such an abelian surface is isomorphic to E×E, where E is an elliptic curve. We considered also the questions for curves. For the plane curve with genus 1 we found the Galois group when it has a Galois point, for the space elliptic curve we found it has always Galois lines.