Unisecant curves on a general ruled surface |
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Authors: | Franco Ghione Alexandru T Lascu |
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Institution: | (1) Istituto Matematico, Universitá di Ferrara, 44100 Ferrara, Italy;(2) Département de Mathématiques et de statistique, Université de Montréal, C.P. 6128, Succursale A, H3C 3J7 Montréal, Québec, Canada |
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Abstract: | Let X be an irreducible algebraic curve of genus g smooth and proper over an algebraically closed field k, a locally free sheaf of rank 2 over X, F=P( ) the projective bundle associated to and :F X the canonical projection. Aunisecant curve on F is a curve (effective divisor) C on F such that the intersection number (C, –1(x))=1, x X. Notice that a section of F over X or alternatively a sub-line bundle of means simply an irreducible unisecant curve. We give here some results on unisecant curves on F. In particular we are able to prove C.Segre's result regarding his general surfaces 8]. A more ample account including all the details will appear later. |
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