The Nagata Type Polynomial Automorphisms and Rectifiable Space Lines

REFERENCES

• Abhyankar , S. S. ( 1977 ). On the semigroup of a meromorphic curve. I . in Proceedings of the International Symposium on Algebraic Geometry, Kyoto Univ., Kyoto , 249 – 414 , Kinokuniya Book Store , Tokyo .
   Google Scholar
• Abhyankar , S. S. , Moh , T. T. ( 1975 ). Embeddings of the line in the plane . J. Reine Angew. Math. 276 : 148 – 166 .
   Web of Science ®Google Scholar
• Bhatwadekar , S. M. , Roy , A. ( 1991 ). Some results on embedding of a line in 3-space . J. Algebra 142 : 101 – 109 .
   Web of Science ®Google Scholar
• Craighero , P. C. ( 1985 ). About Abhyankar's conjectures on space lines . Rend. Sem. Mat. Univ. Padova 74 : 115 – 122 .
   Google Scholar
• Craighero , P. C. (1986). A result on m-flats in . Rend. Sem. Mat. Univ. Padova 75:39–46.
   Google Scholar
• Craighero , P. C. ( 1988 ). A remark on Abhyankar's space lines . Rend. Sem. Mat. Univ. Padova 80 : 87 – 93 .
   Google Scholar
• Ishii , T. ( 2013 ). Construction of wild space lines (Japanese) . Master's Thesis Tokyo Metropolitan University ,
   Google Scholar
• Jelonek , Z. ( 1987 ). The extension of regular and rational embeddings . Math. Ann. 277 : 113 – 120 .
   Web of Science ®Google Scholar
• Kaliman , S. ( 1991 ). Extensions of isomorphisms between affine algebraic subvarieties of k n to automorphisms of k n . Proc. Amer. Math. Soc. 113 : 325 – 334 .
   Web of Science ®Google Scholar
• Kuroda , S. Wildness of polynomial automorphisms in three variables . arXiv:math.AC/1110.1466v1 .
   Google Scholar
• Nagata , M. ( 1972 ). On Automorphism Group of k[x, y] . Lectures in Mathematics, Department of Mathematics, Kyoto University, Vol. 5, Kinokuniya Book-Store Co. Ltd. , Tokyo .
   Google Scholar
• Shastri , A. R. ( 1992 ). Polynomial representations of knots . Tohoku Math. J . 44 : 11 – 17 .
   Web of Science ®Google Scholar
• Shestakov , I. , Umirbaev , U. ( 2004 ). The tame and the wild automorphisms of polynomial rings in three variables . J. Amer. Math. Soc. 17 : 197 – 227 .
   Web of Science ®Google Scholar
• Srinivas , V. ( 1991 ). On the embedding dimension of an affine variety . Math. Ann. 289 : 125 – 132 .
   Web of Science ®Google Scholar
• Suzuki , M. ( 1974 ). Propriétés topologiques des polynomes de deux variables complexes, et automorphismes algébriques de l'espace C 2 . J. Math. Soc. Japan 26 : 241 – 257 .
   Google Scholar
• Communicated by J.-J. Yu.
   Google Scholar