Abstract
Martin-Deschamps and Perrin proved upper bounds on the dimensions of the first cohomology group of each twist of the ideal sheaf of a locally Cohen-Macaulay space curve of degree d and genus g. When these upper bounds are not all zero, the curves which achieve equality for all twists are extremal curves. We show that connected extremal curves are self-linked if and only if the characteristic of the ground field is two, extending results of Migliore who proved the case of double lines.
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Acknowledgements
I want to thank Scott Nollet for all his helpful comments and guidance. I would also like to thank the referee for their useful comments, especially those regarding Corollary 3.7.
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Aguirre, L. On self-linkage of extremal curves. Arch. Math. 121, 39–46 (2023). https://doi.org/10.1007/s00013-023-01868-9
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DOI: https://doi.org/10.1007/s00013-023-01868-9