Numerically special varieties

Abstract: Campana introduced the class of special varieties as the varieties admitting no maps onto an orbifold of general type. They are also characterized by the non-existence of Bogomolov sheaves which are rank one coherent subsheaves of maximal Kodaira dimension in some exterior power of the cotangent bundle. Campana has conjectured that one can replace the Kodaira dimension by the numerical dimension in this characterization. We prove partially this conjecture showing that a projective manifold admitting a rank one coherent subsheaf of the cotangent bundle with numerical dimension 1 is not special. This is a joint work with J.V. Pereira and F. Touzet.

algebraic geometryalgebraic topologycomplex variablesdifferential geometrygeometric topologymetric geometryquantum algebrarepresentation theory

Audience: researchers in the topic

Sapienza A&G Seminar

Series comments: Weekly research seminar in algebra and geometry.

"Sapienza" Università di Roma, Department of Mathematics "Guido Castelnuovo".