Algebraic geometry I - Curves

MATH-328

Media

MATH-328 Algebraic Curves

Live Session Week 13

04.06.2021, 12:04

Week 13

02.06.2021, 13:37

Elliptic curves

Week 12 Live Session

28.05.2021, 11:55

Week 12.2

26.05.2021, 13:36

Proof of Cayley-Bacharach, applications and elliptic curves

Week 12.1

26.05.2021, 13:35

Proof of Bézout's theorem and Cayley-Bacharach

Week 11 Live Session

21.05.2021, 12:09

Week 11.2

19.05.2021, 13:35

Projective plane curves and Bézout's theorem

Week 11.1

19.05.2021, 13:35

Proof of theorem 4.5 part 5

Live Session Week 10

14.05.2021, 11:55

Week 10.2

11.05.2021, 23:40

Computing intersection numbers

Week 10.1

11.05.2021, 23:40

Intersection numbers and their properties

Week 9 Live Session

07.05.2021, 11:48

Week 9.2

05.05.2021, 13:58

DVR's

Week 9.1

05.05.2021, 13:57

Proof the theorem 4.2 on multiplicities

Week 8 Live Session

30.04.2021, 11:50

Week 8.2

28.04.2021, 11:30

Multiplicities of plane curves

Week 8.1

28.04.2021, 11:30

Week 7 Live Session

23.04.2021, 12:02

Week 7.2

21.04.2021, 13:10

Dimension of an algebraic variety

Week 7.1

21.04.2021, 13:10

Field of rational functions for general varieties

Live Session Week 6

16.04.2021, 10:47

Week 6.2

14.04.2021, 13:37

Morphisms and general local rings

Week 6.1

14.04.2021, 13:36

Algebraic varieties and morphisms

Week 5 Live Session

26.03.2021, 11:49

Week 5.2

24.03.2021, 12:24

Projective algebraic sets and the definition of an algebraic variety.

Week 5.1

24.03.2021, 12:24

Projective space and projective algebraic sets

Live Session Week 4

19.03.2021, 11:45

Week 4.2

17.03.2021, 12:13

Regular functions on quasi-affine varieties

Week 4.1

17.03.2021, 12:12

Morphisms between affine algebraic varieties

Live Session Week 3

12.03.2021, 11:50

Algebraic varieties in linear algebra

Week 3.2

10.03.2021, 11:54

Affine algebraic varieties

- Zariski Topology

- Regular functions of affine algebraic varieties

Week 3.1

10.03.2021, 11:53

Irreducible algebraic sets 

Live session 05.03.2021

05.03.2021, 11:43

Recap on algebraic subsets of A^1 and idelas with a finite set of points

Week 2.2

03.03.2021, 12:50

Hilberts Nullstellensatz and ideals with finite sets of points

Week 2.1

03.03.2021, 12:49

Affine algebraic sets

Week 1

24.02.2021, 10:28

Recollections from commutative algebra


This file is part of the content downloaded from Algebraic geometry I - Curves.

This course gives an introduction to algebraic geometry with a highlight on algebraic curves. The rough outline of the course is

  • Affine algebraic sets
  • Affine algebraic varieties
  • (Quasi)projective varieties
  • Local study of plane curves
  • Projective plane curves and Bézout's theorem

References


The course and exercices will be held in-person only:

  • Course on Tuesdays 15:15-17:00 in Room MAA330
  • Exercices on Wednesdays 14:15-16:00 in Room MAA330

Here you can find notes and recordings from a previous year, although we might have slightly different content this year.



Easter break: there will be no course and no TA this week, but a multiple choice quiz on Moodle.

There will be no exercise sheet this week, but the exercise session can be used to as an opportunity to ask questions about the course material. 

Exam

Date: June 25 and 26, 2025.

Room: MA A1 12

Duration: 25 minutes, no preparation time.

Content: The course material plus the exercises in the list below.

Schedule: See the PDF below.