On the birationality of the adjunction mapping of projective varieties

Details On the birationality of the adjunction mapping of projective varieties On the birationality of the adjunction mapping of projective varieties

2011-09-12

arxiv.org/abs/1109.2439v1

Mathematics

Algebraic Geometry

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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