In this thesis I consider Weyl classes on a complex manifold M as introduced by M. Kato. A fundamental fact used by Kato is the existence of a normal reduced projective connection on M: however the proof of this fact is not correct as we demonstrate by way of an example. We also provide a rigorous proof of this fact. Weyl classes give obstructions for the existence of affine or projective structures (holomorphic connection in the K\"{a}hler case) on M. For n >= 3 only partial results are known. The computation of these invariants tends to be rather involved: here we consider some 3-folds whose Weyl classes do not vanish, computing them from different points of view. In particular we consider certain blowing-up non-K\"{a}hler manifolds. This study is related to the open problem of the eventual vanishing of Weyl classes in presence of a holomorphic projective connection.

Classi di Weyl di varieta' complesse

PAMBIANCO, Fernanda
1996

Abstract

In this thesis I consider Weyl classes on a complex manifold M as introduced by M. Kato. A fundamental fact used by Kato is the existence of a normal reduced projective connection on M: however the proof of this fact is not correct as we demonstrate by way of an example. We also provide a rigorous proof of this fact. Weyl classes give obstructions for the existence of affine or projective structures (holomorphic connection in the K\"{a}hler case) on M. For n >= 3 only partial results are known. The computation of these invariants tends to be rather involved: here we consider some 3-folds whose Weyl classes do not vanish, computing them from different points of view. In particular we consider certain blowing-up non-K\"{a}hler manifolds. This study is related to the open problem of the eventual vanishing of Weyl classes in presence of a holomorphic projective connection.
1996
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1037665
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