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June 21
12.00 Hacker
13.15 Daniloff
14.30 Skauli
15.45 Helle

June 22
09.00 Maugesten 
10.15 Gammelgaard
11.30 H?glend
14.00 Vodrup
15.15 Pauli

I have written a short note summarizing the topics covered in the course. (Link in the column to the right).

I've added a short chapter on sheaf cohomology on affine schemes and Pⁿ.

I've added a new chapter on the Proj-construction and morphisms to projective space. 

I've also added some material on separated and proper morphisms, and more on the subscheme-ideal sheaf correspondence.

As ever, the notes can be found here:

Lecture notes - MAT4215

Problem 4(iii) has been changed to involve `ringed spaces' rather than `locally ringed spaces'.

In Problem 5, you can choose whether you want to regard A^2 as a scheme or an affine variety. A few words about how to define the group action in the scheme case has been added to the text.

A few more chapters have been added to the lecture notes.

The mandatory assignment is now out:

Mandatory assignment 

The problems marked with * are not required.

Deadline: Thursday May 12th.

(A first version of) Chapter 3 on gluing schemes is now ready: 

Lecture notes - MAT4215 

I'm currently preparing a set of lecture notes for the course (starting from Geir Ellingsrud's excellent notes from last year). They can be found here:

Lecture notes - MAT4215.

I'll try to update them regularly as we progress with the course.

Note: I'd be very glad to get some feedback on the notes along the way. In particular, if there is something unclear or could be presented in a better way, please feel free to let me know. Also, I'm sure there are several typos in there, any help in resolving them would be greatly appreciated!

Welcome to the course MAT4215 - Algebraic geometry II. 

The course will give an introduction to scheme theory for the most part following Chapters II and III in Hartshorne. 

Preliminary objectives of the course:

• Sheaves. Understand the key examples and how do computations with them. 
• Schemes. Understand their definition, and why they form the correct generalization of varieties. 
• Geometric properties of schemes and morphisms between them.
• The Proj-construction. Understand the sheaf O(1) and modules on Proj(S).
• Equivalence of line bundles, divisors and invertible sheaves. Maps to projective space. 
• Differentials, the (co)tangent bundle, and the canonical divisor. Emphasis on the case of curves. 
• Sheaf cohomology. Cohomology groups of projective space. Cech cohomology.
• If time permits: Serre duality. Riemann-Roch for curves.