Journal of the Ramanujan Mathematical Society

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On the Birationality of the Adjunction Mapping of Projective Varieties


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1 Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen, Norway
     

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Let X be a smooth projective n-fold such that q(X) = 0 and L a globally generated, big line bundle on X such that h0(KX +(n−2)L) > 0. We give necessary and sufficient conditions for the adjoint systems |KX + kL| to be birational for k ≥ n − 1. In particular, for Calabi-Yau n-folds we generalize and prove parts of a conjecture of Gallego and Purnaprajna.
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  • On the Birationality of the Adjunction Mapping of Projective Varieties

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Authors

Andreas Leopold Knutsen
Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen, Norway

Abstract


Let X be a smooth projective n-fold such that q(X) = 0 and L a globally generated, big line bundle on X such that h0(KX +(n−2)L) > 0. We give necessary and sufficient conditions for the adjoint systems |KX + kL| to be birational for k ≥ n − 1. In particular, for Calabi-Yau n-folds we generalize and prove parts of a conjecture of Gallego and Purnaprajna.