Geodesic
Numerical invariants of families of lines on some Fano varieties
Sbornik. Mathematics, Tome 44 (1983) no. 2, pp. 239-260

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It is known that one-dimensional families of lines lie on irrational Fano 3-folds of index 1. These families, which are the object of study in this paper, can be used to describe the birational geometry of the varieties themselves. The author computes such invariants as the genus of the parametrizing curve, the degree of the ruled surface swept out by the lines, and the number of lines lying on the variety and intersecting a given line. The theory of Chern characteristic classes and the Schubert calculus on Grassmannians are used in the computations. Bibliography: 13 titles. 
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     author = {D. G. Markushevich},
     title = {Numerical invariants of families of lines on some {Fano} varieties},
     journal = {Sbornik. Mathematics},
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     number = {2},
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D. G. Markushevich. Numerical invariants of families of lines on some Fano varieties. Sbornik. Mathematics, Tome 44 (1983) no. 2, pp. 239-260. http://geodesic.mathdoc.fr/item/SM_1983_44_2_a7/