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Secant varieties of Grassmann varieties


Authors: M. V. Catalisano, A. V. Geramita and A. Gimigliano
Journal: Proc. Amer. Math. Soc. 133 (2005), 633-642
MSC (2000): Primary 14M15, 15A75
DOI: https://doi.org/10.1090/S0002-9939-04-07632-4
Published electronically: October 7, 2004
MathSciNet review: 2113908
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the dimensions of the higher secant varieties of the Grassmann varieties. We give new instances where these secant varieties have the expected dimension and also a new example where a higher secant variety does not.


References [Enhancements On Off] (What's this?)

  • 1. J.Alexander, A.Hirschowitz. Polynomial interpolation in several variables. J. of Alg. Geom. 4 (1995). 201-222. MR 1311347 (96f:14065)
  • 2. P. Bürgisser, M. Clausen, M.A. Shokrollahi, Algebraic Complexity Theory, Vol. 315, Grund. der Math. Wiss., Springer, 1997. MR 1440179 (99c:68002)
  • 3. M.V.Catalisano, A.V.Geramita, A.Gimigliano. Ranks of tensors, Secant Varieties of Segre Varieties and Fat Points. Lin. Algebra and Appl. 355 (2002). 263-285. MR 1930149 (2003g:14070)
  • 4. M.V.Catalisano, A.V.Geramita, A.Gimigliano. Erratum of the Publisher to: ``Ranks of tensors, Secant Varieties of Segre Varieties and Fat Points". Lin. Algebra and Appl. 367 (2003). 347-348. MR 1976931
  • 5. R.Ehrenborg. On Apolarity and Generic Canonical Forms. J. of Algebra 213 (1999). 167-194. MR 1674676 (2000a:15050)
  • 6. J. Harris, Algebraic Geometry, a first course, Springer, New York, 1993. MR 1182558 (93j:14001)
  • 7. D.R.Grayson, M.E.Stillman, Macaulay 2, a software system devoted to supporting research in algebraic geometry, www.math.uiuc.edu .
  • 8. D. Yu. Nogin. Spectrum of codes associated with the Grassmannian G(3,9). Problems of Information Transmission, 33 (1997). 114-123. MR 1663924 (2000e:94066)
  • 9. F.Palatini. Sulle varietà algebriche per le quali sono di dimensione minore dell' ordinario, senza riempire lo spazio ambiente, una o alcuna delle varietà formate da spazi seganti. Atti Accad. Torino Cl. Scienze Mat. Fis. Nat. 44 (1909). 362-375.
  • 10. A.Terracini. Sulle $V_{k}$ per cui la varietà degli $S_{h}$ $(h+1)$-seganti ha dimensione minore dell'ordinario. Rend. Circ. Mat. Palermo 31 (1911). 392-396.
  • 11. W.Wakeford. On canonical forms. Proc. London Math. Soc. 18 (1919/20). 403-410.
  • 12. F.L.Zak. Tangents and Secants of Algebraic Varieties. Translations of Math. Monographs, vol. 127 AMS. Providence (1993). MR 1234494 (94i:14053)

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Additional Information

M. V. Catalisano
Affiliation: DIPEM, Facoltá di Ingegneria, Università di Genova, Italy
Email: catalisano@dipem.unige.it

A. V. Geramita
Affiliation: Dipartimento di Matematica, Università di Genova, Italy — and — Department of Mathematics and Statistics, Queens’ University, Kingston, Ontario, Canada
Email: geramita@dima.unige.it

A. Gimigliano
Affiliation: Dipartimento di Matematica and CIRAM, Università di Bologna, Italy
Email: gimiglia@dm.unibo.it

DOI: https://doi.org/10.1090/S0002-9939-04-07632-4
Received by editor(s): November 26, 2002
Received by editor(s) in revised form: October 2, 2003
Published electronically: October 7, 2004
Additional Notes: The first author was supported in part by MIUR funds
The second author was supported in part by MIUR funds, and by the Natural Sciences and Engineering Research Council of Canada.
The third author was supported in part by the University of Bologna, funds for selected research topics, and by MIUR funds
Communicated by: Michael Stillman
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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