Logarithmic geometry is a variant of algebraic geometry where on top of the usual algebraic aspect, we add an additional framework: the “logarithmic structure”. It was developed to deal with two fundamental and related problems in algebraic geometry, compactification and degeneration. It aims to provide a language that incorporates various previous constructions in a functorial and systematic way.
During the talk we will see “logarithmic geometry in action” to tackle the question of existence of smoothing for some mildly singular varieties, called normal crossing varieties. I will introduce the necessary notions and give the geometric ideas behind the proofs.