Messages
Read the document "towards final exam", it will help you prepare for the exam. All references are to the first version (not the updated version) of the textbook.
Let me know by Monday March 4th, which of the dates (19.3 and 5.4) you prefer. I will then set up a plan for each day.
The week 4.3-7.3 I will discuss Bezouts theorem, starting will all ingredients. (This will include the later part of ch 10). In week 11-14.3 I will discuss applications (ch 12) and review main topics in the course.
Kristian R
In the lecture Feb 22, we defined the tangent space and non-singularity for points on a variety. We will continue Feb 26, with ch 8, including how blowup can be used to desingularize plane curves.
28.-29 will will also discuss curves (chapter 9).
Final exam will be on March 19. and April 5. Let me know by email, which one you choose.
Remember the deadline, March 1. to give the compulsory presentation. I will provide a list of topics for the final exam after that deadline.
KR
we will cover chapters 7 and 8, but start Monday with example 6.17 og exercise 6.2.
K R
We will cover chapters 5 and 6.1 and start Monday with a warmup on exercises 4.6 and 4.15.
KR
29.1-1.2: I lectured on chapter 3 , with the subsection on consequences starting p 69 left.
Monday 5.2 we will work our way through exercises
3.5,3.8,3.12. prop 3.75 and its corollaries and 4.1.
Wednesday and Thursday 7.-8.2 we will do 4.2-4.3.
Kristian R
Possibly in pairs, present in up to 20 min one of the following (the list may be extended):
1. Exercise 1.11 (affine normal rational curve X), and show that X is determinental algebraic set.
2. Exercise 2.11 + generalization from 3 variables, to n variables.
3. Prop 2.62 (the set of (m x n)- matrices of rank at most r is irreducible)
4. Prop 2.64 (the set of quadratic forms in n variables of rank at most r is irreducible)
5. Prop 5.16. (d+3 general points in d-space lies on a unique rational normal curve of degree d)
6. Prop 5.20 Segre product is a projective variety
7. The 5.31. Hilbert Nullstellensatz in the product of projective space.
At most one pair for each topic, on a first come first serve order. Send an email to me when you have decided, and I will approve what is not taken and we find a date for the presentation.
Kristian R
I will lecture on 2.3,2.4 and 3.1,3.2.
I will also discuss (Monday) examples 2.19,2.20 and exercise 2.1
Kristian
Welcome to the course MAT4210 - Algebraic Geometry I.
We will be using the following text:
Introduction to Algebraic geometry
First lecture is 15.1.2024 in room 1120 at 1415.
Kristian R