Abhyankar–Moh theorem

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.

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, http://www.digizeitschriften.de/dms/img/?PID=GDZPPN002190885 .
• Hazewinkel, Michiel, ed. (2001), "Abhyankar–Moh theorem", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=A/a120010