Abhyankar–Moh theorem

In mathematics, the Abhyankar–Moh theorem states that if ${\displaystyle L}$ is a complex line in the complex affine plane ${\displaystyle \mathbb {C} ^{2}}$, then every embedding of ${\displaystyle L}$ into ${\displaystyle \mathbb {C} ^{2}}$ 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.

References

• Abhyankar, Shreeram S.; Moh, Tzuong-Tsieng (1975), "Embeddings of the line in the plane", Journal für die reine und angewandte Mathematik, 276: 148–166, MR 0379502.
• M. Hazewinkel (2001) [1994], "Abhyankar–Moh theorem", Encyclopedia of Mathematics, EMS Press