A characterization of the Veronese surface

Ballico, Edoardo

doi:10.1090/S0002-9939-1989-0953737-5

A characterization of the Veronese surface
HTML articles powered by AMS MathViewer

by Edoardo Ballico

Proc. Amer. Math. Soc. 105 (1989), 531-534

DOI: https://doi.org/10.1090/S0002-9939-1989-0953737-5

PDF | Request permission

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.

References

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, DOI 10.1007/978-1-4757-5323-3
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 10.1007/BFb0083331

On Reider’s method and higher embeddings

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, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York, 1978. 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