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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Uniqueness of varieties of minimal degree containing a given scheme

Author: M. Casanellas
Journal: Trans. Amer. Math. Soc. 356 (2004), 1875-1888
MSC (2000): Primary 14M06, 14M12, 14M05
Published electronically: October 8, 2003
MathSciNet review: 2031044
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Abstract: We prove that if $X \subset \mathbb{P} ^N$ has dimension $k$ and it is $r$-Buchsbaum with $r>\max{(\operatorname{codim}{X}-k,0)}$, then $X$ is contained in at most one variety of minimal degree and dimension $k+1$.

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  • 1. J.N. Brawner, Tetragonal curves, rational normal scrolls and K3 surfaces, Trans. Amer. Math. Soc. 349 (1997), 3075-3091. MR 97j:14056
  • 2. M. Casanellas, Characterization of non-connected Buchsbaum curves in $\mathbb{P} ^n$, Le Matematiche (Catania) LIV (1999), 187-195. MR 2001j:14063
  • 3. -, Teoria de liaison en codimensió arbitrària, Ph.D. thesis, Universitat de Barcelona, 2002.
  • 4. M. Casanellas and R.M. Miró-Roig, Gorenstein liaison and special linear configurations, Illinois Math. J. 46 (2002), 129-143. MR 2003i:14062
  • 5. D. Eisenbud and J. Harris, On varieties of minimal degree (A centennial account), Algebraic Geomtery, Bowdoin 1985, Amer. Math. Soc. Symp. in Pure and App. Math. (S. Bloch, ed.), vol. 46, 1985, pp. 3-14. MR 89f:14042
  • 6. J. Harris, A bound on the geometric genus of projective varieties, Ann. Scuola Norm. Sup. Pisa (4) 8 (1981), 35-68. MR 82h:14010
  • 7. L.T. Hoa, R.M. Miró-Roig, and W. Vogel, On numerical invariants of locally Cohen-Macaulay schemes in $\mathbb{P} ^n$, Hiroshima Math. J. 24 (1994), 299-316. MR 95m:14031
  • 8. J. Kleppe, J. Migliore, R.M. Miró-Roig, U. Nagel, and C. Peterson, Gorenstein liaison, complete intersection liaison invariants and unobstructedness, Memoirs A.M.S. 732 (2001). MR 2002e:14083
  • 9. J. Lesperance, Gorenstein liaison of some curves in $\mathbb{P} ^4$, Collectanea Mathematica 52 (2001), 219-230. MR 2003g:14065
  • 10. J. Migliore, Geometric invariants for liaison of space curves, J. Alg. 99 (1986), 548-572. MR 87g:14031
  • 11. -, Liaison of a union of skew lines in $\mathbb{P} ^4$, Pacific J. of Math. 130 (1987), 153-170. MR 88j:14041
  • 12. -, Introduction to liaison theory and deficiency modules, Progress in Mathematics, no. 165, Birkhäuser, 1998. MR 2000g:14058
  • 13. J. Migliore and U. Nagel, Liaison and related topics, Rend. Sem. Mat. Univ. Pol. Torino 59 (2001), 59-126.
  • 14. C. Miyazaki, Sharp bounds on Castelnuovo-Mumford regularity, Trans. Amer. Math. Soc. 352 (1999), 1675-1686. MR 2000i:13017

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Additional Information

M. Casanellas
Affiliation: Departament d’Algebra i Geometria, Facultat de Matematiques, Universitat de Barcelona, Gran Via 585, 08007-Barcelona, Spain

Received by editor(s): August 5, 2002
Published electronically: October 8, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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