- Lecturer
- Maria Yakerson
- Coordinator
- Younghan Bae

This course is an Introduction to Algebraic Geometry. The course will mostly cover algebraic varieties (over algebraically closed fields), with some scheme theory towards the end of the course. It is required to have a basic knowledge of Commutative Algebra.

Algebra, Commutative Algebra courses.

Lecture notes will be uploaded every week.

- Chapter 0 - Introduction
- Chapter 1 - Algebraic sets
- Chapter 2 - Zariski topology
- Chapter 3 - Sheaves and varieties
- Chapter 4 - Projective varieties
- Chapter 5 - Dimension revisited
- Chapter 6 - Smoothness and singularities
- Chapter 7 - Birationality
- Chapter 8 - Curves
- Chapter 9 - Properties of morphisms
- Chapter 10 - Bezout theorem (note by John Ottem)
- Chapter 11 - Prime spectrum
- Chapter 12 - Schemes
- Chapter 13 - The Weil conjecture

The new exercises will be posted here on Wednesdays. We expect you to try to solve the problems and prepare questions for the exercise class on Tuesday.

exercise sheet | due by | Notes |
---|---|---|

Exercise sheet 1 | March 1 | |

Exercise sheet 2 | March 8 | Note 2 |

Exercise sheet 3 | March 15 | Note 3 |

Exercise sheet 4 | March 22 | Note 4 |

Exercise sheet 5 | March 22 | Note 5 |

Exercise sheet 6 | March 29 | Note 6 |

Exercise sheet 7 | April 06 | Note 7 |

Exercise sheet 8 | April 20 | Note 8 |

Exercise sheet 9 | April 27 | Note 9 |

Exercise sheet 10 | May 04 | Note 10 |

Exercise sheet 11 | May 11 | Note 11 |

Exercise sheet 12 | May 18 | Note 12 |

Exercise sheet 13 | May 18 | Note 13 |

Jeremy Feusi kindly agree to share his solutions.

time | room | assistant | language |
---|---|---|---|

Tu 12-13 | HG D 1.1 | Younghan Bae | English |

Primary References:

- Introduction to Algebraic Varieties by Geir Ellingsrud and John Ottem (lecture note)
- Algebraic Geometry by James Milne
- The Geometry of Schemes David Eisenbud and Joe Harris
- Introduction to schemes by Geir Ellingsrud and John Ottem

Secondary References:

- Undergraduate algebraic geometry by Miles Reid
- Foundations of Algebraic Geometry by Ravi Vakil

Other References

- Algebraic Geometry and Arithmetic Curves by Qing Liu
- Algebraic Geometry I by Ulrich Gortz and Torsten Wedhorn
- Basic Algebraic geometry I, II by Igor Shafarevich
- Algebraic Geometry by Robin Hartshorne