A speciality theorem for Cohen-Macaulay space curves

Schlesinger, Enrico

doi:10.1090/S0002-9947-99-02435-6

A speciality theorem for Cohen-Macaulay space curves
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by Enrico Schlesinger

Trans. Amer. Math. Soc. 351 (1999), 2731-2743

DOI: https://doi.org/10.1090/S0002-9947-99-02435-6

Published electronically: February 23, 1999

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Abstract:

We prove a version of the Halphen Speciality Theorem for locally Cohen-Macaulay curves in $\mathbb {P}^3$. To prove the theorem, we strengthen some results of Okonek and Spindler on the spectrum of the ideal sheaf of a curve. As an application, we classify curves $C$ having index of speciality as large as possible once we fix the degree of $C$ and the minimum degree of a surface containing $C$.

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