Algebraic Geometry

Spring 2016

Faculty of Science, Department of Mathematics, Room: SA-121, Phone: 1490

Office Hours: Tuesday 10:40-12:00 or by appointment

THU 10:40-12:30 SBZ-11

Hartshorne's book is famous, or notorious, for the difficulty of its exercises. For this reason there are numerous alleged solutions floating on internet, mostly wrong!

After we solve some exercises and discuss the others I will assign some of the discussed but not solved exercises as homework or midterm exam depending on the complexity of the exercise.

You may choose your own homework or midterm exam exercise yourself after consulting with me.

Overall I expect to collect, during the 15 week semester, 2 midterm exams and 4 homework problems. That makes one written and submitted work for every other week. The final exam will be again one particularly involved exercise of your own choice and of my approval.

a) Exercises I.3.7 page 21

b) On top of page 32 Hartshorne says "One can show easily that this definition of nonsingularity is independent of the set of generators of the ideal of Y chosen." Prove this claim.

Everybody chose and solved one exercise which interested them the most.

Exercise I.3.20(a) page 23.

a) Exercise 7.1 page 54

b) Exercise 7.2 page 54.

Active class participation and regular handing in of written work will be recognized as a sign of achievement at the time of letter grading.

Date | Hours | Topics | Section |
---|---|---|---|

28 January 2016 | 2 |
Affine Varieties | 1 |

2-4 February 2016 |
3 |
Exercises |
1 |

9-11 February 2016 |
3 |
Pojective Varieties |
2 |

16-18 February 2016 |
3 |
Exercises |
2 |

23-25 February 2016 |
3 |
Morphisms |
3 |

1-3 March 2016 |
3 |
Exercises |
3 |

8-10 March 2016 |
3 |
Rational Maps |
4 |

15-17 March 2016 |
3 |
Exercises | 4 |

22-24 March 2016 |
3 |
Non-singular Varieties |
5 |

29-31 March 2016 |
3 |
Exercises | 5 |

5-7 April 2016 |
3 |
Non-singular Curves |
6 |

12-14 April 2016 |
3 |
Exercises | 6 |

19-21 April 2016 |
3 |
Intersections in Projective Space |
7 |

26-28 April 2016 |
3 |
Exercises | 7 |

3 May 2016 |
1 |
What to expect in MATH 592 |
8 |

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