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arXiv · 1109.2439

On the birationality of the adjunction mapping of projective varieties

Andreas Leopold Knutsen
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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 $h^0(K_X+(n-2)L) >0$. We give necessary and sufficient conditions for the adjoint systems $|K_X+kL|$ to be birational for $k \geq n-1$. In particular, for Calabi-Yau $n$-folds we generalize and prove parts of a conjecture of Gallego and Purnaprajna.

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Andreas Leopold Knutsen. 2011-09-12. On the birationality of the adjunction mapping of projective varieties. https://arxiv.org/abs/1109.2439

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