Cycle Algebraic Geometry 2021-2023 

Algebraic Geometry I (Winter Semester 2021/2022)

The Notes. 

The Problem Sheets. 

Table of contents:

1. The Nullstellensatz

2. The Zariski Topology

3. Sheaves

4. Varieties

5. Projective Varieties

6. Projective Constructions: Segre and Veronese embeddings

7. Dimension Theory

8. Smoothness and Blowups

9. Curves

10. Bezout's Theorem and Applications

11. Divisors and Elliptic Curves

Algebraic Geometry II (Summer Semester 2022)

The Notes. 

The Problem Sheets. 

Table of contents:

1. Schemes

2. Projective Schemes

3. Sheaves of Modules

4. Quasi-Coherent Sheaves

5. Properties of Schemes

6. Weil and Cartier Divisors

7. Kähler Differentials

Algebraic Geometry III (Winter Semester 2022/2023)

The Notes. 

The Problem Sheets. 

Table of contents:

1. Cech Cohomology

2. Cohomology of Projective Space & Examples

3. Cohomology via Derived Functors

4. Morphisms to Projective Space

5. Flatness and Families of Varieties

6. Curves

7. Surfaces

Algebraic Geometry IV (Summer Semester 2023)

This was a seminar with student talks and discussion sessions. The program. We covered the following three topics:

1. Classification of algebraic surface.

2. Intersection theory.

3. Deformation theory.