Projective algebraic geometry and its applications

The lectures will take place live on zoom on June 8,10,12, 2020, 14:30 - 16:30, and will cover the last part of the course "Algebraic Geometry".

 

Abstract: 
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The aim of the series of lectures is to explain projective geometry and, as an application, basic facts about the Krull dimensions of algebraic varieties. 

I will discuss in detail projective spaces, (quasi-)projective varieties and the homomorphisms between these. I will explain the projective elimination theorem and its consequence - each homomorphism from a projective variety has a Zariski closed image. 

Finally, I will explain the concept of Krull dimension and establish basic properties - among them proving that the affine space A^n and the projective space P^n have the expected Krull dimension n.