Algebraic Geometry Spring 2024

Lecturer
Johannes Schmitt
Coordinator
Dmitrii Krekov

News

Content

The lecture follows very closely the lecture notes by Andreas Gathmann. In particular it covers

Prerequisites

Properties of commutative rings and modules over them (as covered by the lecture Commutative Algebra).

Format

The lecture is offered in a flipped classroom setup:

Feedback

Since the format of the course is pretty new, I am always happy for feedback! You can submit it either via email or via this (anonymous) form.

Lectures

Overview

You find the lecture videos on youtube.

Week Material
1 01.01 Affine varieties - 02.03 Irreducible affine varieties
2 02.04 Noetherian spaces and irreducible decompositions - 02.09 Dimension theory of reducible spaces
3 03.01 Definition of regular functions - 04.02 Properties of morphisms of ringed spaces
4 04.03 Morphisms between affine varieties - 05.05 Products of prevarieties
5 05.06 Separatedness and the definition of varieties - 06.11 The projective closure
6 06.12 Projective hypersurfaces - 07.06 Complete varieties
7 07.07 The Veronese embedding - 09.01 Rational and birational maps
8 09.02 Rational functions - 09.08 Blowing up to remove indeterminacies of rational maps
9 10.01 The tangent space to a variety - 11.01 The lines on the Fermat cubic surface
10 11.02 The moduli space of smooth cubic surfaces - 12.05 Regular functions and the structure sheaf of affine schemes
11 12.06 Regular functions on distinguished open sets - 12.14 Definition of schemes
12 12.15 Schemes from prevarieties - 13.05 The tensor presheaf
13 13.06 Sheafification - 14.05 Properties of pullback sheaves
14 14.06 Locally free sheaves - 15.04 Application - the genus of a smooth projective curve (optional: Epilogue - What next)

Whiteboard notes

Exercises

The new exercises will be posted here on Fridays. We expect you to look at the problems over the weekend and to prepare questions for the exercise class on Monday.

Please hand in your solutions by the following Friday at 12:00 in your assistant's box in HG J68. Your solutions will usually be corrected and returned in the following exercise class or, if not collected, returned to the box in HG J68.

exercise sheet due by solutions
Exercise sheet 1 February 23 Solution 1
Exercise sheet 2 March 1 Solution 2
Exercise sheet 3 March 8 Solution 3
Exercise sheet 4 March 15 Solution 4
Exercise sheet 5 March 22 Solution 5
Exercise sheet 6 March 29 Solution 6
Exercise sheet 7 April 12 Solution 7
Exercise sheet 8 April 19 Solution 8
Exercise sheet 9 April 26 Solution 9
Exercise sheet 10 May 3 Solution 10
Exercise sheet 11 May 10 Solution 11
Exercise sheet 12 May 17 Solution 12
Exercise sheet 13 May 24 Solution 13
Exercise sheet 14 May 31
live problem sheet date solutions
Sheet 1 February 27 Solution 1
Sheet 2 March 5 Solution 2
Sheet 3 March 12 Solution 3
Sheet 4 March 19 Solution 4
Sheet 5 March 26 Solution 5
Sheet 6 April 9 Solution 6
Sheet 7 April 16 Solution 7
Sheet 8 April 23 Solution 8
Sheet 9 April 30 Solution 9
Sheet 10 May 7 Solution 10
Sheet 11 May 14 Solution 11
Sheet 12 May 21 Solution 12
Sheet 13 May 28 Solution 13

Exercise classes

timeroomassistantlanguage
Mo 16-17HG E 1.2Dmitrii KrekovEnglish

Literature