13/07/2017, 16:00 — 17:00 — Anfiteatro Pa1, Pavilhão de Matemática
Bruno de Oliveira, University of Miami
The geometry of symmetric differentials
Complex manifolds have an array of intrinsic tensors. They provide us with geometric notions with fascinating connections to fundamental algebraic, topological and arithmetic properties. Intrinsic tensors include symmetric differentials which are sections of the symmetric powers of the cotangent bundle. We will discuss three aspects of the algebra of symmetric differentials on projective manifolds. Topology: the mysterious relation between the fundamental group and the algebra of symmetric differentials. Intrinsic analytic and arithmetic geometry: obstructions to the existence of special subvarieties (e.g. rational and elliptic curves). Extrinsic geometry and algebraic properties: submanifolds of low codimension in projective space have no holomorphic symmetric differentials. We describe for low codimensions what is the geometry and the algebraic properties associated to the non-vanishing algebra of symmetric differentials whose poles are of the lowest possible order.
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BO_s.pdf
