Stratification of the Hilbert scheme of space curves with a stable normal bundle

Ford≥3g and 1≤s≤g/2], we study the strataN _{d, g(s)} of degreed genusg spaces curvesC whose normal bundleN _C is stable with stability degree (integer of Lange-Narasimhan) σ(N _C)=2s. We prove thatN _{d, g(s)} has an irreducible component of the right dimension whose general curve has a normal bundle with the right number of maximal subbundles. We consider also the semi-stable case (s=0), obtaining similar results. We prove our results by studying the normal bundles of reducible curves and their deformations. Both authors were partially supported by MIUR and GNSAGA of INdAM (Italy).