Abstract: | In this paper, we study the Hilbert scheme of non degenerate locally Cohen- Macaulay projective curves with general hyperplane section spanning a linear space of dimension 2 and minimal Hilbert function. The main result is that those curves are almost always the general element of a generically smooth component Hn,d,g of the corresponding Hilbert scheme. Moreover, we show that the curves with maximal cohomology almost always correspond to smooth points of Hn,d,g.All the authors were partially supported by Acción Integrada Italia-España, HI2000-0091, and by the Italian counterpart of the project. |