On the real X -ranks of points of P n (R) with respect to a real variety X ⊂ P n

Edoardo Ballico

Annales UMCS, Mathematica (2010)

  • Volume: 64, Issue: 2, page 15-19
  • ISSN: 2083-7402

Abstract

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Let X ⊂ Pn be an integral and non-degenerate m-dimensional variety defined over R. For any P ∈ Pn(R) the real X-rank r x,R(P) is the minimal cardinality of S ⊂ X(R) such that P ∈ . Here we extend to the real case an upper bound for the X-rank due to Landsberg and Teitler.

How to cite

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Edoardo Ballico. " On the real X -ranks of points of P n (R) with respect to a real variety X ⊂ P n ." Annales UMCS, Mathematica 64.2 (2010): 15-19. <http://eudml.org/doc/267900>.

@article{EdoardoBallico2010,
abstract = {Let X ⊂ Pn be an integral and non-degenerate m-dimensional variety defined over R. For any P ∈ Pn(R) the real X-rank r x,R(P) is the minimal cardinality of S ⊂ X(R) such that P ∈ . Here we extend to the real case an upper bound for the X-rank due to Landsberg and Teitler.},
author = {Edoardo Ballico},
journal = {Annales UMCS, Mathematica},
keywords = {Ranks; real variety; structured rank; ranks},
language = {eng},
number = {2},
pages = {15-19},
title = { On the real X -ranks of points of P n (R) with respect to a real variety X ⊂ P n },
url = {http://eudml.org/doc/267900},
volume = {64},
year = {2010},
}

TY - JOUR
AU - Edoardo Ballico
TI - On the real X -ranks of points of P n (R) with respect to a real variety X ⊂ P n
JO - Annales UMCS, Mathematica
PY - 2010
VL - 64
IS - 2
SP - 15
EP - 19
AB - Let X ⊂ Pn be an integral and non-degenerate m-dimensional variety defined over R. For any P ∈ Pn(R) the real X-rank r x,R(P) is the minimal cardinality of S ⊂ X(R) such that P ∈ . Here we extend to the real case an upper bound for the X-rank due to Landsberg and Teitler.
LA - eng
KW - Ranks; real variety; structured rank; ranks
UR - http://eudml.org/doc/267900
ER -

References

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  2. Arbarello, E., Cornalba, M., Griffiths, P. and Harris, J., Geometry of Algebraic Curves. I, Springer-Verlag, New York, 1985. Zbl0559.14017
  3. Ballico, E., Ranks of subvarieties of Pn over non-algebraically closed fields, Int. J. Pure Appl. Math. 61(1) (2010), 7-10. Zbl1203.14061
  4. Ballico, E., Subsets of the variety X ⊂ Pn computing the X-rank of a point of Pn, preprint. 
  5. Bernardi, A., Gimigliano, A. and Idà, M., Computing symmetric rank for symmetric tensors, J. Symbolic Comput. 46 (2011), 34-55.[WoS] Zbl1211.14057
  6. Bochnak, J., Coste, M. and Roy, F.-M., Real Algebraic Geometry, Translated from the 1987 French original. Revised by the authors. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 36, Springer-Verlag, Berlin, 1998. 
  7. Buczyński, J., Landsberg, J. M., Ranks of tensors and a generalization of secant varieties, arXiv:0909.4262v1 [math. AG].[WoS] Zbl1268.15024
  8. Comas, G., Seiguer, M., On the rank of a binary form, arXiv:math. AG/0112311.[WoS] Zbl1211.14059
  9. Comon, P., Golub, G., Lim, L.-H. and Mourrain, B., Symmetric tensors and symmetric tensor rank, SIAM J. Matrix Anal. Appl. 30(3) (2008), 1254-1279. Zbl1181.15014
  10. Hartshorne, R., Algebraic Geometry, Springer-Verlag, Berlin, 1977. 
  11. Landsberg, J. M., Teitler, Z., On the ranks and border ranks of symmetric tensors, Found. Comput. Math. 10 (2010), 339-366.[WoS] Zbl1196.15024
  12. Lang, S., Algebra, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965. 

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