Abstract
On the one hand this note complements the results obtained in [2] for rational curves, and, on the other hand, it introduces the study of the normal bundle of a curve of arbitrary genus in IP3 (the projective space over an algebraically closed field of characteristic 0). The most important result concerns rational curve; we give the dimension of the variety parametrizing rational curve of fixed degree and fixed normal bundle, and we show they are quasi-projective, integral and Cohen-Macaulay.
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