Algebraic Geometry I

Prerequisites (besides linear algebra) are only the contents of Algebra I [1]. The lecture Algebra II [2] is helpful but not necessary.

We offer oral exams (duration: 45 minutes) on the following dates:

Here is the Complete Table of Contents [7].
The lecture mainly follows the script by Andreas Gathmann [8], focussing on:

• affine and projective varieties
• morphisms
• dimension theory
• tangent spaces
• degree

Henning Seidler's notes on this lecture and many other awesome lecture notes can be found here [9].

There are exercise sheets available which are not graded or marked:

• Sheet 1 [10]
• Sheet 2 [11]
• Sheet 3 [12]
• Sheet 4 [13] - Solutions [14]
• Sheet 5 [15]
• Sheet 6 [16]
• Sheet 7 [17]
• Sheet 8 [18]
• Sheet 9 [19]
• Sheet 10 [20]
• Sheet 11 [21]
• Sheet 12 [22]
• Sheet 13 [23]

• Shafarevich - Basic Algebraic Geometry 1
• Brodmann - Algebraische Geometrie: Eine Einführung
• Fulton - Algebraic Curves
• Harris - Algebraic Geometry: A First Course (viele konkrete Beispiele)
• Hartshorne - Algebraic Geometry (Kapitel 1)
• Kunz - Einführung in die algebraische Geometrie
• Mumford - The red book of varieties and schemes (Kapitel 1)
• Reid - Undergraduate Algebraic Geometry (elementar)