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In mathematics, the Abhyankar–Moh theorem states that if L is a complex line in the complex affine plane \( \mathbb{C}^2 \), then every embedding of L into \(\mathbb{C}^2 \) extends to an automorphism of the plane. It is named after Shreeram Shankar Abhyankar and T.-T. 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", J. Reine Angew. Math. 276: 148–166, MR 379502.
M. Hazewinkel (2001), "Abhyankar–Moh theorem", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4

Mathematics Encyclopedia

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