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A characterization of the Veronese surface


Author: Edoardo Ballico
Journal: Proc. Amer. Math. Soc. 105 (1989), 531-534
MSC: Primary 14J25; Secondary 14M05
DOI: https://doi.org/10.1090/S0002-9939-1989-0953737-5
MathSciNet review: 953737
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Abstract: Here we prove a slight modification of a conjecture of Beltrametti-Sommese proving that the Veronese surface and a general intersection of 3 quadrics are the only smooth surfaces of ${\mathbf {CP}^5}$ which are $2$-spanned.


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  • E. Arbarello, M. Cornalba, P. A. Griffiths, and J. Harris, Geometry of algebraic curves. Vol. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 267, Springer-Verlag, New York, 1985. MR 770932
  • Mauro Beltrametti and Andrew J. Sommese, On $k$-spannedness for projective surfaces, Algebraic geometry (L’Aquila, 1988) Lecture Notes in Math., vol. 1417, Springer, Berlin, 1990, pp. 24–51. MR 1040549, DOI https://doi.org/10.1007/BFb0083331
  • M. Beltrametti, P. Francia, A. J. Sommese, On Reider’s method and higher embeddings, preprint.
  • Michel Demazure, Henry Charles Pinkham, and Bernard Teissier (eds.), Séminaire sur les Singularités des Surfaces, Lecture Notes in Mathematics, vol. 777, Springer, Berlin, 1980 (French). Held at the Centre de Mathématiques de l’École Polytechnique, Palaiseau, 1976–1977. MR 579026
  • Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Wiley-Interscience [John Wiley & Sons], New York, 1978. Pure and Applied Mathematics. MR 507725
  • Steven L. Kleiman, The transversality of a general translate, Compositio Math. 28 (1974), 287–297. MR 360616
  • Patrick Le Barz, Formules multisécantes pour les courbes gauches quelconques, Enumerative geometry and classical algebraic geometry (Nice, 1981), Progr. Math., vol. 24, Birkhäuser, Boston, Mass., 1982, pp. 165–197 (French). MR 685769

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Article copyright: © Copyright 1989 American Mathematical Society