Algebraic geometry, Fall 2016

Reading course at JGU, Mainz.

The lectures are given on **Thursdays, 12 -- 14**.

The lectures are held in **Room 04.516**.

The course is intended as a starting course in Algebraic Geometry and it is aimed to bachelor and master students who are familiar with commutative algebra.

During the course we will follow Robin Hartshorne's book `Algebraic Geometry'.

The aim of the course is to study in detail the first two chapters of the book, discussing the proofs of the results and solving, or trying to solve, the exercises.

Once solved, the solutions of the exercise will be published on this website, for future memory.

The course is also a place where to discuss the content of Manfred Lehn's course `Invariant theory'. During the course the students will be welcome to ask questions about Lehn's classes. For this reason Lehn's student are particularly encouraged to follow the course.

We shall follow Hartshorne's `Algebraic Geometry' [HAG], the first 2 chapters.

The curious student may also read `The red book of varieties and schemes', by Mumford [MVS].

For reference to commutative algebra, we suggest the book `Introduction to Commutative Algebra', by Atiyah--MacDonald [AM], and/or `Commutative Algebra with a view toward Algebraic Geometry' by Eisenbud [EIS].

Date | Topics | Lecturer | Homework |
---|---|---|---|

November 3rd | Affine spaces and Zariski topology: definitions and first properties [HAG, I.1]. | Dino | |

November 10th | Until [HAG, Corollary I.1.6] | Davide | [HAG, Exercises I.1.1--I.1.7, I.1.12] |

November 17th | No class. | ||

November 24th | Until the end of [HAG, I.1] | Dino | [HAG, I.1.8--I.1.11]. Exercise I.1.10 is due for the next week. |

December 1st | [HAG, I.2] | Davide | [HAG, I.2.1--I.2.5]. It is compulsory to hand in at least two of them, freely chosen, next Thursday. |

December 8th | [HAG, Exercises I.1.2.6, 9, 10] | Dino | [HAG, Exercises I.1.2.7, 8, 11] |

December 15th | Until [HAG, Theorem I.3.2], excluded. | Davide | [HAG, I.2.16 and I.2.17]. |

December 22th | [HAG, Section I.3] | Dino | [HAG, Exercises I.3.1--4] |

January 12 | [HAG, Section I.3] | Davide | [HAG, Exercises I.3.1--4] |

January 19 | Quartic forms over P^1 | Dino | [HAG, Exercises I.3.1--4] |

January 26 | Introduction to Elliptic Curves | Dino | [HAG, Exercises I.3.1--4] |

February 2 | [HAG, Section I.3] | Davide | [HAG, Exercises I.3.1--4] |

February 9 | Introduction to Schemes | Davide |