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A Step in Castelnuovo theory via Grobner bases

We establish the first previously unknown case of the Eisenbud-Harris conjecture in Castelnuovo theory concerning algebraic curves of high genus in Pn{\bf P}^n. The problem is reduced to a question about zero-dimensional schemes ΓPn1\Gamma \subset {\bf P}^{n-1} in symmetric position with certain constrains on the Hilbert function. The method of Gr\"obner bases is then applied to study the homogeneous ideal of Γ\Gamma.
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Published on April 24, 2006
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