On the birationality of the adjunction mapping of projective varieties

Andreas Leopold Knutsen

On the birationality of the adjunction mapping of projective varieties

Algebraic Geometry 2011-09-13 v1

Authors: Andreas Leopold Knutsen

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.

Keywords

adjunction mapping birationality projective varieties line bundles calabi-yau n-folds adjoint systems

Cite

@article{arxiv.1109.2439,
  title  = {On the birationality of the adjunction mapping of projective varieties},
  author = {Andreas Leopold Knutsen},
  journal= {arXiv preprint arXiv:1109.2439},
  year   = {2011}
}

Comments

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

On the birationality of the adjunction mapping of projective varieties

Abstract

Keywords

Cite

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