| We establish the first previously unknown case of the Eisenbud-Harris conjecture in Castelnuovo theory concerning algebraic curves of high genus in Pn. The problem is reduced to a question about zero-dimensional schemes Gamma⊂ P n-1 in symmetric position with certain constrains on the Hilbert function. The method of Grobner bases is then applied to study the homogeneous ideal of Gamma.; Also, we study moduli of "self-associated" sets of points in projective spaces of small dimensions. |
