manuscripta mathematica

, Volume 62, Issue 4, pp 417–435

Smooth surfaces of degree 9 in G(1,3)

Authors

  • Alessandro Verra
    • Istituto di Matematica, Facoltà di ArchitetturaUniversità di Napoli
Article

DOI: 10.1007/BF01357719

Cite this article as:
Verra, A. Manuscripta Math (1988) 62: 417. doi:10.1007/BF01357719

Abstract

Let S⊂G(1,3)⊂p5 be a smooth, irreducible, non degenerate surface in the complex grassmannian G(1,3). Assume deg(S)=9, we show that S is one of the following surfaces:
  1. (a)

    A K3 surface blown up in one point.

     
  2. (b)

    The image of P2 by the linear system\(\left| {O_{P^2 } (6) - 2b_1 - \ldots - 2b_5 - b_6 - \ldots - b_{12} } \right|\)

     
  3. (c)

    The image of P2 by the linear system\(\left| {O_{P^2 } (7) - 2b_1 - \ldots - 2b_{10} } \right|\).

     
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© Springer-Verlag 1988