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On varieties with locally free logarithmic tangent sheaf

Le : 23/03/2018 14h00
Par : Hannah Berger (Université de Freiburg)
Lieu : I 001
Lien web :
Résumé : 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.