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

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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.