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A Step in Castelnuovo theory via Grobner bases

Ivan Petrakiev
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Abstract

We 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 $Γ$.

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Ivan Petrakiev. 2006-04-24. A Step in Castelnuovo theory via Grobner bases. https://arxiv.org/abs/math/0604517

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