Oliver Lindström: Blow-Ups in Real and Complex Geometry

The Blow-Up of a scheme in a closed subscheme is a well known and very powerful tool in algebraic geometry. Among other things it can be used for the resolution of singularities of a variety which reduces many problems about varieties to the smooth case. In this talk we will introduce the analogous notions of complex and real, oriented, blow-ups of a topological space in a section of a vector bundle. We will show that for complex varieties these blow-ups satisfy some particularly nice properties. Finally, we will briefly explain how real, oriented, blow-ups can be used to define the Kato-Nakayama analytification of a so called log-scheme.