, Volume 62, Issue 4, pp 417-435

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

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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 K3 surface blown up in one point.

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