#### Lectures in mathematics : Kyoto University

##### vol. 5

On automorphism group of k[x, y] / by Masayoshi Nagata

c1972

Part 0 Introduction and Preliminaries | 1 |

Introduction | 1 |

0.2 Some easy results related to the statements in Introduction | 5 |

0.3 The easy case, n = 1 | 7 |

0.4 Prerequisites, notation and terminology | 7 |

0.5 Infinitely near points | 9 |

Part 1 The case n = 2 and k is a field | 18 |

1.1 A preliminary step | 18 |

1.2 Geometric proof of (1.8) | 21 |

1.3 Remarks to the proof | 28 |

1.4 Another proof | 32 |

1.5 One question on rational curves | 38 |

Part 2 Questions in the general case | 41 |

2.1 An example | 41 |

2.2 Another example | 44 |

2.3 The case of three or more variables | 47 |

2.4 One more question | 51 |

References | 53 |