Blowing-ups along closed subschemes and examples

Abstract

The aim of the thesis is to study various properties and examples of blowing-ups. First, we define blowing-ups of varieties, complex manifolds, and schemes. In the later case, we have a beautiful construction by using global Proj, so we focus on blowing-ups of schemes along closed subschemes. Next, we explain useful properties to compute explicit formula for blowing-ups, and describe interesting examples algebraically and geometrically.