A Step in Castelnuovo theory via Grobner bases

Abstract

We establish the first previously unknown case of the Eisenbud-Harris conjecture in Castelnuovo theory concerning algebraic curves of high genus in ${\mathbf{P}}^n$. The problem is reduced to a question about zero-dimensional schemes $\Gamma \subset {\mathbf{P}}^{n-1}$ in symmetric position with certain constrains on the Hilbert function. The method of Gröbner bases is then applied to study the homogeneous ideal of $\Gamma$.

24 pages

Cited by in corpus (1)

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