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The tangent bundle of a ruled surface. (English) Zbl 0541.14035
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.

MSC:
14J25 Special surfaces
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14J17 Singularities of surfaces or higher-dimensional varieties
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