Abhyankar–Moh theorem

Every embedding of a complex line into the complex affine plane extends to an automorphism

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