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

E. Ballico 1  and C. Fontanari 1
  • 1 University of Trento


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.

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  • [1] B. Ådlandsvik: “Joins and higher secant varieties”, Math. Scand., Vol. 61, (1987), pp. 213–222.

  • [2] J. Alexander and A. Hirschowitz: “Polynomial interpolation in several variables”, J. of Alg. Geom., Vol. 4 (1995), pp. 201–222.

  • [3] J. Alexander and A. Hirschowitz: “An asymptotic vanishing theorem for generic unions of multiple points”, Invent. Math., Vol. 140, No. 2, (2000), pp. 303–325. http://dx.doi.org/10.1007/s002220000053

  • [4] E. Ballico: “On the secant varieties to the tangent developable of a Veronese variety”, preprint, (2003).

  • [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.

  • [6] J. Chipalkatti: “Tangential envelopes of Veronese varieties”, preprint, http://www.mast.queensu.ca/jaydeep/.

  • [7] C. Ciliberto and A. Hirschowitz: “Hypercubiques de P 4 avec sept points singuliers génériques”, C. R. Acad. Sci. Paris Sér. I Math., Vol. 313, No. 3., (1991), pp. 135–137.

  • [8] C. Ciliberto and R. Miranda: “Interpolations on curvilinear schemes”, J. Algebra, Vol. 203, No. 2, (1998), pp. 677–678. http://dx.doi.org/10.1006/jabr.1997.7241

  • [9] M. Dale: “Severi’s theorem on the Veronese-surface”, J. London Math. Soc., Vol. 32, (1985), pp. 419–425.

  • [10] C. Dionisi and C. Fontanari: “Grassmann defectivity à la Terracini”, preprint, math.AG/0112149, (to appear on Le Matematiche).

  • [11] A. Eastwood: “Collision de biais et application a l’interpolation”, Manuscripta Math., Vol. 67, (1990), pp. 227–249.

  • [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

  • [13] G. Hardi: “Rational varieties satisfying one or more Laplace equations”, Ricerche Mat., Vol. 8, (1999), pp. 123–137.

  • [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


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