# On Self-Intersection Number of a Section on a Ruled Surface

@article{Nagata1970OnSN, title={On Self-Intersection Number of a Section on a Ruled Surface}, author={M. Nagata}, journal={Nagoya Mathematical Journal}, year={1970}, volume={37}, pages={191-196} }

Let E be a non-singular projective curve of genus g ≥ 0, P the projective line and let F be the surface E× P . Then it is well known that a ruled surface F* which is birational to F is biregular to a surface which is obtained by successive elementary transformations from F (for the notion of an elementary transformation, see [3]).

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