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manuscripta mathematica

, Volume 62, Issue 2, pp 227–244 | Cite as

On the adjunction process over a surface in char.p

  • M. Andreatta
  • E. Ballico
Article

Abstract

Let Ks be the canonical bundle on a non singular projective surface S (over an algebraically closed field F, char F=p) and L be a very ample line bundle on S. Suppose (S,L) is not one of the following pairs: (P2,O(e)), e=1,2, a quadric, a scroll, a Del Pezzo surface, a conic bundle. Then
  1. 1)

    (Ks⊗L)2 is spanned at each point by global sections. Let\(\phi :S \to P^N _F \) be the map given by the sections Γ(Ks⊗L)2, and let φ=s o r its Stein factorization.

     
  2. 2)

    r:S→S′=r(S) is the contraction of a finite number of lines, Ei for i=1,...r, such that Ei·Ei=KS·Ei=−L·Ei=−1.

     
  3. 3)

    If h°(L)≥6 and L·L≥9, then s is an embedding.

     

Keywords

Finite Number Line Bundle Number Theory Algebraic Geometry Topological Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • M. Andreatta
    • 1
    • 2
  • E. Ballico
    • 1
    • 2
  1. 1.Dipartimento di MatematicaUniversitá di MilanoMilanoItalia
  2. 2.Dipartimento di MatematicaUniversità di TrentoPovoItalia

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