On linking double lines
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- by Juan Migliore PDF
- Trans. Amer. Math. Soc. 294 (1986), 177-185 Request permission
Abstract:
A double line is a nonreduced locally Cohen-Macaulay scheme of degree two supported on a line in projective three-space. The heart of this work is to compute the associated Hartshorne-Rao module for such a curve. We can then say exactly when two such curves are in the same liaison class and in fact when they are directly linked. In particular, we find that $C$ is only self-linked in characteristic two.References
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A. Geramita, P. Maroscia and W. Vogel, On curves linked to lines in ${{\mathbf {P}}^3}$, The Curves Seminar at Queen’s, II, Queen’s Papers in Pure and Applied Math., vol. 61, Kingston, Ontario, 1982, pp. B1-B26.
—, A note on arithmetically Buchsbaum curves in ${{\mathbf {P}}^3}$, Queen’s University Preprint No. 1983-24.
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- Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
- Juan Migliore, Geometric invariants for liaison of space curves, J. Algebra 99 (1986), no. 2, 548–572. MR 837562, DOI 10.1016/0021-8693(86)90045-1 P. Rao, Liaison among curves in ${{\mathbf {P}}^3}$, Invent. Math. 50 (1979), 205-217.
- A. P. Rao, On self-linked curves, Duke Math. J. 49 (1982), no. 2, 251–273. MR 659940
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 294 (1986), 177-185
- MSC: Primary 14H45; Secondary 14M05
- DOI: https://doi.org/10.1090/S0002-9947-1986-0819941-3
- MathSciNet review: 819941