The tangent bundle of a ruled surface (Q794731)

Let Z be a ruled surface. The authors settle, in the case of decomposable Z, the questions of existence and classification of sublinebundles of the tangent bundle \(T_ Z\). They also show, in the indecomposable case, that \(T_ Z\) splits in general in the sense of moduli (if the ground field has characteristic not 2). The ''integrable'' sublinebundles of \(T_ Z\) give rise to ''quotient'' surfaces Y of Z, which exhibit various interesting ''pathological'' features. One obtains, for instance, surfaces Y of general type with global vector fields. These quotient surface examples were worked out in collaboration with H. Kurke; a more detailed analysis of them is forthcoming.