On the secant varieties to the osculating variety of a Veronese surface

E. Ballico; C. Fontanari

Open Mathematics (2003)

  • Volume: 1, Issue: 3, page 315-326
  • ISSN: 2391-5455

Abstract

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In this paper we study the k-th osculating variety of the order d Veronese embedding of P n. In particular, for k=n=2 we show that the corresponding secant varieties have the expected dimension except in one case.

How to cite

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E. Ballico, and C. Fontanari. "On the secant varieties to the osculating variety of a Veronese surface." Open Mathematics 1.3 (2003): 315-326. <http://eudml.org/doc/268805>.

@article{E2003,
abstract = {In this paper we study the k-th osculating variety of the order d Veronese embedding of P n. In particular, for k=n=2 we show that the corresponding secant varieties have the expected dimension except in one case.},
author = {E. Ballico, C. Fontanari},
journal = {Open Mathematics},
keywords = {14N05},
language = {eng},
number = {3},
pages = {315-326},
title = {On the secant varieties to the osculating variety of a Veronese surface},
url = {http://eudml.org/doc/268805},
volume = {1},
year = {2003},
}

TY - JOUR
AU - E. Ballico
AU - C. Fontanari
TI - On the secant varieties to the osculating variety of a Veronese surface
JO - Open Mathematics
PY - 2003
VL - 1
IS - 3
SP - 315
EP - 326
AB - In this paper we study the k-th osculating variety of the order d Veronese embedding of P n. In particular, for k=n=2 we show that the corresponding secant varieties have the expected dimension except in one case.
LA - eng
KW - 14N05
UR - http://eudml.org/doc/268805
ER -

References

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  4. [4] E. Ballico: “On the secant varieties to the tangent developable of a Veronese variety”, preprint, (2003). 
  5. [5] M.V. Catalisano, A.V. Geramita, A. Gimigliano: “On the secant variety to the tangential varieties of a Veronesean”, Proc. Amer. Math. Soc., Vol. 130, No. 4, (2001), pp. 975–985. Zbl0990.14021
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  9. [9] M. Dale: “Severi’s theorem on the Veronese-surface”, J. London Math. Soc., Vol. 32, (1985), pp. 419–425. Zbl0597.14030
  10. [10] C. Dionisi and C. Fontanari: “Grassmann defectivity à la Terracini”, preprint, math.AG/0112149, (to appear on Le Matematiche). 
  11. [11] A. Eastwood: “Collision de biais et application a l’interpolation”, Manuscripta Math., Vol. 67, (1990), pp. 227–249. Zbl0722.41010
  12. [12] A. Hirschowitz: “La méthode d’Horace pour l’interpolation à plusieurs variables’, Manuscripta Math., Vol. 50, (1985), pp. 337–378. http://dx.doi.org/10.1007/BF01168836 Zbl0571.14002
  13. [13] G. Hardi: “Rational varieties satisfying one or more Laplace equations”, Ricerche Mat., Vol. 8, (1999), pp. 123–137. Zbl0961.14034
  14. [14] F. Severi: “Intorno ai punti doppi impropri di una superficie generale dello spazio a quattro dimensioni, e ai suoi punti tripli apparenti”, Rend. Palermo, Vol. 15, (1901), pp. 33–51. http://dx.doi.org/10.1007/BF03017734 Zbl32.0648.04

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