**Topics**

Hilbert’s basis theorem, Hilbert‘s Nullstellensatz, (quasi-)affine and (quasi-)projective varieties, dimension, Zariski topology, local rings, morphisms and rational maps, blow-ups smoothness, intersection multiplicities, Bézout‘s theorem, plane curves and resolution of singularities, divisors and the Riemann-Roch theorem for curves

**Literature**

- Atiyah McDonald, Introduction to commutative Algebra,
- R. Hartshorne, Algebraic Geometry, Springer.
- K. Hulek Elementary Algebraic Geometry,
- M. Reid, Undergraduate Algebraic Geometry

Links to the books are found here.

**Dates**

Lecture 1: Tuesdays 10:15 - 11:45, MS-Teams

Lecture 2: Thursdays 10:15 - 11:45, MS-Teams

Exercise session, to be announced, MS-Teams;

Office hours: by appointment