Abhyankar–Moh theorem

From HandWiki
Short description: Every embedding of a complex line into the complex affine plane extends to an automorphism

In mathematics, the Abhyankar–Moh theorem states that if [math]\displaystyle{ L }[/math] is a complex line in the complex affine plane [math]\displaystyle{ \mathbb{C}^2 }[/math], then every embedding of [math]\displaystyle{ L }[/math] into [math]\displaystyle{ \mathbb{C}^2 }[/math] extends to an automorphism of the plane. It is named after Shreeram Shankar Abhyankar and Tzuong-Tsieng Moh, who published it in 1975. More generally, the same theorem applies to lines and planes over any algebraically closed field of characteristic zero, and to certain well-behaved subsets of higher-dimensional complex affine spaces.