Séminaire de géométrie algébrique

# Hannah Bergner (Université de Freiburg) On varieties with locally free logarithmic tangent sheaf

Europe/Paris
I 001 (Angers)

### I 001

#### Angers

Description
Let (X,D) be a pair consisting of a normal complex variety and a divisor D. In the talk, I would like to investigate the relation between the geometry of (X,D) and properties of the logarithmic vector fields on X, or dually the logarithmic 1-forms. If X is smooth and D is snc, then the logarithmic tangent sheaf is locally free. More generally, this holds true if X is toric. In the talk, I will explain a theorem about the local converse of this statement, i.e. in which cases local freeness of the the logarithmic tangent sheaf implies that X has to be locally toric.