Introduction to Algebraic Geometry with a View Toward Hilbert Schemes

Abstract: In this bachelor’s thesis an introduction to the fundamentals of algebraic geometry is given. Some concepts in algebraic geometry are introduced such as Spec of a ring and Proj of a graded ring and several results related to these are either proven or stated. Special focus is directed towards defining the so called ”Hilbert scheme” which is the main topic in a lot of modern algebraic geometry research.