In this work we 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.
On Weyl classes on compact manifolds
PAMBIANCO, Fernanda
2002
Abstract
In this work we 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
