Math 431 Algebraic Geometry

Fall 2002

Solutions

**Instructor: **Ali Sinan
Sertöz, Department of Mathematics

**Room:** SA-121, **Phone:** 1490

**Office Hours: **Tuesday 13:40-15:30

**Text: **Philip A. Griffiths, Introduction to Algebraic Curves, American
Mathematical Society, 1989.

**Schedule:**

MONDAY | 13:40-15:30 | SAZ-19 |

WEDNESDAY | 14:40-15:30 | SAZ-19 |

**Topics: **

- Algebraic plane curves and Riemann surfaces. (Chapter I)
- Singularities and normalization. (Chapter II)
- Riemann-Roch theorem. (Chapter III)
- Abel's theorem. (Chapter IV)

**Syllabus:**

1 |
23 Sep-25 Sep | Algebraic Curves in the plane: I.1,
I.2, I.3 |

2 |
30 Sep-2 Oct | Functions and forms: I.4, I.5, I.6 |

3 |
7 Oct-9 Oct | Complex manifolds: I.7, I.8, I.9, I.10 |

4 |
14 Oct-16 Oct | Singular curves: II.1, II.2, II.3 |

5 |
21 Oct-23 Oct | Normalization theorem: II.4, II.5, II.6 |

6 |
28 Oct-30 Oct | Bezout's theorem: II.7, II.8, II.9 |

7 |
4 Nov-6 Nov | Differentials: III.1, III.2, III.3 |

8 |
11 Nov-13 Nov | Riemann-Roch theorem: III.4, III.5 |

9 |
18 Nov-20 Nov | Curves of genus 0 and 1: IV.1, IV.2 |

10 |
25 Nov-27 Nov | Canonical maps: IV.3, IV.4 |

11 |
2 Dec (Wed!) | Hyperelliptic curves: IV.5, IV.6, IV.7 |

12 |
9 Dec-11 Dec | Abel's theorem: V.1 |

13 |
16 Dec-18 Dec | Riemann bilinear relation: V.2, V.3 |

14 |
23 Dec-25 Dec | Jacobi inversion theorem: V.4 |

15 |
30 Dec | Applications: V.5 |

**How to study:
**Read the text lightly first. Then study the

**Grading:
**Homework I (10%): Due on 11 October 2002 Friday.
Solution

Homework II (10%): Due on 1 November 2002 Friday. Solution

Homework III (10%): Due on 3 January 2003 Friday. Solution

Midterm I (20%): On 2 November 2002 Saturday. Solution

Midterm II (20%): On 14 December 2002 Saturday. Solution

Final (30%): On 8 January 2002 Wednesday Solution

15:30 : SAZ-19