2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111674We establish the first previously unknown case of the Eisenbud-Harris conjecture in Castelnuovo theory concerning algebraic curves of high genus in ${\bf P}^n$. The problem is reduced to a question about zero-dimensional schemes $Γ\subset {\bf P}^{n-1}$ in symmetric position with certain constrains on the Hilbert function. The method of Gröbner bases is then applied to study the homogeneous ideal of $Γ$.24 pagesAlgebraic GeometryCommutative Algebra14N05, 14H50text