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Biliaison classes of curves in ${\mathbf{P}}^{3}$

Author: Rosario Strano
Journal: Proc. Amer. Math. Soc. 132 (2004), 649-658
MSC (2000): Primary 14H50; Secondary 14H45
Published electronically: July 31, 2003
MathSciNet review: 2019939
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Abstract: We characterize the curves in ${\mathbf{P}}^{3}$ that are minimal in their biliaison class. Such curves are exactly the curves that do not admit an elementary descending biliaison. As a consequence we have that every curve in ${\mathbf{P}}^{3}$ can be obtained from a minimal one by means of a finite sequence of ascending elementary biliaisons.

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  • [1] M. Amasaki, On the structure of arithmetically Buchsbaum curves in ${\mathbf{P}}^{3}_{k}$, Publ. Res. Inst. Math. Sci. 20 (1984), 793-837. MR 86a:14027
  • [2] E. Ballico, G. Bolondi, and J. C. Migliore, The Lazarsfeld-Rao problem for liaison classes of two-codimensional subschemes of ${\mathbf{P}}^{n}$, Amer. J. Math. 113 (1991), 117-128. MR 92c:14047
  • [3] R. Lazarsfeld and A. P. Rao, Linkage of general curves of large degree, Lecture Notes in Math. 997 (1983). MR 85d:14043
  • [4] S. Mac Lane, Homology, Grundlehren der mathematischen Wissenschaften, Band 114, Springer-Verlag, Berlin, 1967. MR 50:2285
  • [5] M. Martin-Deschamps, Minimalité des courbes sous-canoniques, Ann. Inst. Fourier (Grenoble) 52 (2002), 1027-1040.
  • [6] M. Martin-Deschamps and D. Perrin, Sur la classification des courbes gauches, Astérisque 184-185 (1990). MR 91h:14039
  • [7] R. Maggioni and A. Ragusa, Betti numbers of space curves bounded by Hilbert functions, Le Matematiche 52 (1997), 217-232. MR 99e:14035
  • [8] J. C. Migliore, Introduction to Liaison Theory and Deficiency Modules, Birkhäuser, Boston, 1998. MR 2000g:14058
  • [9] A. P. Rao, Liaison among curves in ${\mathbf{P}}^{3}$, Inventiones Math. 50 (1979), 205-217. MR 80e:14023
  • [10] E. Schlesinger, The spectrum of projective curves, Ph.D. Thesis, U. C. Berkeley, 1996.

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Additional Information

Rosario Strano
Affiliation: Department of Mathematics and Informatics, University of Catania, Viale A. Doria 6, I95125 Catania, Italy

Keywords: Space curves, liaison, elementary biliaison, minimal curves
Received by editor(s): June 10, 2002
Received by editor(s) in revised form: October 25, 2002
Published electronically: July 31, 2003
Additional Notes: This work was done with the financial support of the MIUR (Italian Research Ministry)
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2003 American Mathematical Society

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