The lecture notes were prepared by Kartik Venkatram in collaboration with Professor Kumar.

LEC # | TOPICS | LECTURE NOTES |
---|---|---|

1 | Introduction | (PDF) |

2 | Linear equivalence, algebraic equivalence, numerical equivalence of divisors | (PDF) |

3 | Birational maps, rational maps, linear systems, properties of birational maps between surfaces | (PDF) |

4 | Birational maps (cont.) | (PDF) |

5 | Ruled surfaces I | (PDF) |

6 | Ruled surfaces II | (PDF) |

7 | Ruled surfaces III, rational surfaces | (PDF) |

8 | Linear systems, rational normal scrolls | (PDF) |

9 | Castelnuovo’s criterion for rationality | (PDF) |

10 | Picard variety | (PDF) |

11 | Albanese variety | (PDF) |

12 | Non-ruled and ruled surfaces | (PDF) |

13 | Classification of ruled surfaces | (PDF) |

14 | Elliptic and quasi-elliptic surfaces | (PDF) |

15 | Elliptic surfaces (cont.), Kodaira dimension 0 | (PDF) |

16 | K3 surfaces | (PDF) |

17 | Enriques surfaces, bielliptic surfaces | (PDF) |

18 | Classification | (PDF) |

19 | Elliptic/quasi-elliptic fibrations I | (PDF) |

20 | Elliptic/quasi-elliptic fibrations II | (PDF) |

21 | Elliptic/quasi-elliptic fibrations III, classification | (PDF) |

22 | Classification (cont.) | (PDF) |

23 | Moduli |