## On automorphism group of k[x, y] |

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### Contents

Introduction and Preliminaries | 1 |

The case n 2 and k is a field | 18 |

Questions in the general case | 41 |

Copyright | |

1 other sections not shown

### Common terms and phrases

a e Aut affine line affine transformation Assume Aut k[x automorphism group automorphism of k[x bf(ax birational correspondence birational transformation biregular c e k coefficient common point complete the proof Conjecture 3.l consider Cq+l defined denote dilp divisorial cycles e k[x effective transform effectively positive element of Aut fibre fixed component fixed point function field fundamental points fundamental with respect GL(n ground field hence homogeneous form hyperplane at infinity infinitely near point integral domain intersection multiplicity intersection number irreducible curve irreducible member isomorphism Jonquieres transformation k-automorphism k-homomorphism k-rational Lemma l.l linear system linear transformation locus of g m-ple point Masayoshi NAGATA minimal section module natural numbers nilpotent non-singular projective surfaces one-place point ordinary point points with respect polynomial ring positive divisors proof of l.8 proper transform Proposition 5.4 question 0.3 Remark 5.ll sequence subgroup of Aut Theorem 3.3 total transform virtue z(zx