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In particular, we show that for  degree $4g+4$, the highest degree for which interesting deformations exist, the number of smoothing components is $2^{2g+1}$ ($g\\neq3$).\n  We review in a general setting the relation of $T^1(-1)$ with Wahl's Gaussian map. We prove that $T^1(-1)$ vanishes for a general curve and an arbitrary embedding line bundle of degree at least $2g+11$. 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