On the birationality of the adjunction mapping of projective varieties

Mathematics – Algebraic Geometry

Scientific paper

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7 pages, accepted for publication in Journal of the Ramanujan Mathematical Society

Scientific paper

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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